text: (km 2, cm 2, mm 2) Fill in all the gaps, then press "Check" to check your answers. Tuesday 14th Worksheets For Sixth Grade Math. Proving triangle congruence worksheet Get a free sample copy of our Math Salamanders Dice Games book Math worksheets: Convert lengths (mm, cm, m and km) Below are six versions of our grade 6 math worksheet on converting common metric units of length (mm, cm, m and km). open the link below to use while you make your calculations. They will need to learn how to convert fractions, square roots, temperatures, speed and more. Types of angles worksheet. Unit Conversion Worksheet Answers one of Education Template - ideas, to explore this Unit Conversion Worksheet Answers idea you can browse by and . Customary units worksheet. Convert units word problems (metrics) Our mission is to provide a free, world-class education to anyone, anywhere. Hometuition-kl - Letter Tracing Worksheets PDF. Label answers with the appropriate unit of measure. The sheets have been designed for children working at a 3rd or 4th grade level. Worksheets > Math > Grade 6 > Measurement > Convert metric units - mixed practice. Converting Units – Length, Area, Volume (Metric) From the red Metric conversions table, we can see that there are three different length unit conversions we need to know, \text{\textcolor{red}{mm}} to \text{\textcolor{blue}{cm}} to \text{\textcolor{limegreen}{m}} to \text{\textcolor{purple}{km}} and vice versa.. Welcome to how to Convert Metric Units of Length with Mr. J! Customary units worksheet. 5 MD A 1 Metric Conversion Word Problems from Converting Metric Units Worksheet With Answers Sum of the angles in a triangle is 180 degree worksheet. Get all of Hollywood.com's best Celebrities lists, news, and more. Welcome to our Metric Conversion Worksheets page. As well as converting between different metric units, the sheets on this page will also help children to practice multiplying by 10, 100 or 1000 in meaningful context. English Worksheets For Kids. Calculate the following, and write your answer to each in scientific notation. Create Spelling Worksheets. 5-a-day GCSE 9-1; 5-a-day Primary ; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. These worksheets are great practice for first grade, second grade, third grade and fourth grade students and can also provide practical subtraction practice when measuring the length of objects on a ruler. An answer sheet can also be found below. Units: Converting imperial units for capacity Video 348c Practice Questions Celsius to Fahrenheit : (°C × 9/5) + 32 = °F. We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page. ID: 184732 Language: English School subject: Math Grade/level: Grade 4 Age: 7-11 Main content: Convert m, cm and mm Other contents: Add to my workbooks (55) Download file pdf Embed in my website or blog Add to Google Classroom Trigger some interesting practice along the way with this huge compilation of metric unit conversion worksheets comprising a conversion factors cheat sheet, and exercises to convert metric units of length, mass or weight, and capacity. Preview. As a class, work examples of converting body weight in pounds to kilograms and body height in inches to centimeters. %PDF-1.4 Metric units worksheet. On this code-breaker worksheet, students need to convert the metric measurements into the units shown. • Teach students how to convert between customary units and metric units. We hope your happy with this Unit Conversion Worksheet Answers idea. The units of measure in the English and metric systems Most Americans are taught the English or standard system of measurement, but never get a really good dose of the metric system. Welcome to the measurement worksheets page at Math-Drills.com where you can measure up, measure down or measure all around! Khan Academy is a 501(c)(3) nonprofit organization. Converting Weight in Metric & U.S. Converting Units for Areas/Volumes Practice Questions Click here for Questions . Units: Converting imperial units for length Video 348a Practice Questions. Only requires division (no multiplication) except for in the extension section. All Rights Reserved. Math worksheets: Convert metric units of length, volume and weight. customary unit conversions worksheet answer key, metric mania worksheet answer key and metric conversion worksheet are some main things we will present to you based on the post title. Welcome to The Metric Conversion All Length, Mass and Volume Units Mixed (A) Math Worksheet from the Measurement Worksheets Page at Math-Drills.com. This math worksheet was created on 2013-02-14 and has been viewed 188 times this week and 660 times this month. Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child. In a perfect situation, students would be taught the prefixes of the Metric system and their relationships to powers of ten which they could apply to any prefix and any unit. Worksheets are Work 14 using the international system of units si, Unit conversions work 1, Tables of si units and prefixes, Unit 2 measurement, Scientific notation metric system unit conversion, Please let me know if you find any typos in this answer, Converting units of measure, Guide for the use of the international system of units si. <> Each conversion will give them a letter to put in the sentence at the top of the sheet. (adsbygoogle=window.adsbygoogle||[]).push({}); On this webpage, you will find a range of measurement worksheets to help your child learn to convert between different metric units of measurement. Your child can learn, practice and test their year 8 (age 12- 13) skills with these automatically marked, interactive year 8 maths worksheets.We’ve created a range of Key Stage 3 year 8 maths worksheets with answers to help your lesson planning across the full curriculum, to make sure they learn everything they need to know ready for their exams! 1) 0.30 m = mm 2) 5.00 mm = cm 3) 10.0 cm = in 4) 2.00 km = m 5) 33.4 L = mL 6) 15.0 lb = kg (use 2.20 lb = 1 kg) One sample is included in the scenario. Practice … Complementary and supplementary word problems worksheet. © 2010-2021 Math Salamanders Limited. Great for practising converting between metric units. If you need a reminder of the steps, you can download and print this worksheet (Acrobat (PDF) 44kB Apr11 08) walking you through … 4.9 18 customer reviews. Estimation A candy maker buys a bar of chocolate weighing 162 ounces. Have students tie beads in place to represent planetary distances. Related Topics: More Measurement Worksheets Measurement Games . Area and perimeter worksheets. Although the metric system (using SI units) is the standard system of measure in most parts of the world many countries still use at least some of their traditional units of measure. The first of the volume conversion worksheets deals with units that are smaller than a liter milliliters to liters and centiliters to liters. • Teach students how to convert between pounds, ounces, cups, pints, quarts, and gallons. Metric units worksheet. Convert different forms of metric units Mass Capacity Length from Metric Conversion Worksheet With Answers , source: pinterest.com New 2012 12 13 Measurement Worksheet Converting Celsius to from Metric Conversion Worksheet With Answers Complementary and supplementary word problems worksheet. For Activity 1: Provide students with examples of using the metric system and unit conversions in different healthcare contexts. Area and perimeter worksheets. Properties of parallelogram worksheet. how pounds he . convert between different metric measurements for area, interactive mathematics worksheets and solutions. %�쏢 Need help with mm, cm, m, and km conversions? ! Preview and details Files included (1) doc, 26 KB. You can also make worksheets for the metric system: units with the prefixes milli, centi, deci, deka, hecto, and kilo. 5 0 obj Take a look at some more of our worksheets similar to these. Using the sheets in this section will help your child to: Need help with printing or saving? Measurement concepts and skills give students the ability to perform tasks related to everyday life. Bronze, Silver, Gold and Platinum – KS2 questions in increasing difficulty January 1st January Bronze Silver Gold Platinum 2nd January Bronze Silver Gold Platinum … These units are related to each other by a factor of ten. our costs. Today we'd like you to have a look at some tasks on metric units. Videos and Worksheets; Primary; 5-a-day. Created: Mar 9, 2015 No Frills worksheet which only includes cm->m and m->km. Add the 8 oz to 3 lb. Objective: I know how to convert between different metric measurements for area. Saved by Kelli Bassham. Free. The final series of metric conversion worksheets on this page is about conversion of metric volume units. These conversion worksheets have problems with various levels of difficulty converting between imperial (customary) and metric unit of length using unit fractions and unit cancelling. college kids worksheet equation solver. Measuring Worksheet 1 Answer Key Worksheets for all from Converting Metric Units Worksheet With Answers, source: bonlacfoods.com. If you are a regular user of our site and appreciate what we do, For example, a Units: types of metric and imperial unit Video 347 Practice Questions. Fahrenheit to Celsius: (°F − 32) x 5/9 = °C. These time conversion units include conversion from milliseconds to seconds, seconds to minutes, minutes to hours and hours to days. Step 5 As a class, use units of measure to solve contextual problems. Using these metric conversion worksheets will help your child to: We also have a selection of converting worksheets for customary units. Metric Conversions Worksheet – Homeschool Helper Online. The sheets have been carefully graded with the easiest sheets first. 21 best megs metric conversion images on Pinterest from Converting Metric Units Worksheet With Answers, source: pinterest.com. Learning metric units have a whole lot of advantages, it's simple as it's units scale to the power of 10. hours? We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step! Try to do (a)–(i) first without the aid of your calculator, then check your answers by redoing them with your calculator. please consider making a small donation to help us with Using these sheets will help your child understand how to: Using these sheets will help children to consolidate their fractions and place value learning. Looking for a fun and motivating way to learn and practice math skills? Have students complete Worksheet 1. This section contains our 3rd grade time worksheets to help children tell the time in multiples of 5 minutes. An answer sheet is also available for you to check your answers. Step 6 Have students work individually on solving word problems that involve units of measure. Kids Homework Sheets. Step 4 In a group, or with a partner, students will practice converting between different units of measure. There are also sheets for converting betweeen gallons, quarts, pints and cups. Here you will find our range of sheets to support your child in learning to convert between metric units. Customary Systems 5:16 Converting Celsius to Fahrenheit and Back 3:38 Go to 6th-8th Grade Measurement: Units of Measurement Below are six versions of our grade 6 measurement worksheet with mixed practice converting metric units.. Follow these 3 easy steps to get your worksheets printed out perfectly! Similar: Convert metric lengths (with decimals) Convert metric volumes & weights (with decimals) It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone … Circle the largest amount in each box. word equation. The scales include finding the length, weight or liquid capacity. Remember to watch the White Rose video, Lesson 1 on the following link, under the heading Summer Term Week 12, w/c 13th July; before having a go at the worksheet. Create an unlimited supply of worksheets for conversion of metric measurement units or for metric system in general, for grades 2-7. stream Converting between Metric units is really an exercise in multiplying and dividing by powers of ten. Metric Units Conversion Worksheet. Free Downloadable Preschool Activities. Why not try one of our free printable math games with your students! Loading... Save for later. Learn to convert time from one unit to another. Highlight the important words and numbers. Metric Area Conversion. 7. Click here for Answers . Converting Metric and Imperial Units Practice Questions Click here for Questions . You can also customize them using the worksheet generator provided. .�ܿ�We�K�����Hs�.��e��xid�eSe\�IzA��N��r%� ��J�Q,��<7� ����F:Yl_-)Ljz;V5QL��R�KM��L-c��}�[�U���n6�fm���/mp�M�Ʉ_�����%#�Bq����M/�=v��z� ����f�G�\�(e6�8�T��a�LȘQ%�X������q%��&�r���Cu��7���6�q4���������x��V(TMU��*�Ҩ�ʦ��t3��#Cb����:�HWx���pP�U^�lb�^��u���. CONVERTING METRIC UNITS – LENGTH SHEET 1 ANSWERS 1) 1cm = 10 mm 2) 2cm = 20 mm 3) 3cm = 30 mm 4) 4cm = 40 mm 5) 1m = 100 cm 6) 2m = 200 cm 7) 3m = 300 cm 8) 4m = 400 m 9) 1km = 1000 m 10) 2km = 2000 m 11) 3km = 3000 m 12) 4km = 4000 m Which is the most? Conversion between metric and standard units can be tricky since the units of distance, volume, area and temperature can seem rather arbitrary when compared to one another. Convert young mathematicians' knowledge of place value into an understanding of the metric system with this five-lesson unit. with each donation! They are also interactive and will give you immediate feedback, Number, fractions, addition, subtraction, division, multiplication, order of operations, money and time worksheets, with video lessons, examples and step-by-step solutions. These worksheets are pdf files.. Measurement Worksheets Teacher Worksheets School Worksheets Math Teacher Math Classroom Teaching 6th Grade 8th Grade Math Teaching Math Fourth Grade Complementary and supplementary worksheet. Similar: Convert metric lengths (with decimals) Convert metric volumes and weights Students will need a string 4.5 meters long. Read more. This page includes Measurement worksheets for length, area, angles, volume, capacity, mass, time and temperature in Metric, U.S. and Imperial units.. 1 m 1 km 1 cm 10 m 100 cm 200 mm We have added a new feature that allows members who are teachers to easily share access to the Math Antics website with their students at home. View Premium Worksheets . If you do not have a list of common conversion factors in your book, you may wish to download and print this sheet of common conversion factors for the geosciences (Acrobat (PDF) 40kB Sep3 09). Click here for Answers . While we talk about Measuring Units Worksheet Answer Key, below we will see various related images to give you more ideas. Practice unit conversion problems with free time unit conversion worksheets and match the answer with the answer key given at the end of each worksheet. Metric Distance Conversion with Decimal Values - The basic metric units for length are millimeters, centimeters, meters and kilometers. Name: Metric Unit Conversion Worksheet; File Type: JPG; Source: pinterest.com; Size: 143.12 KB; Dimension: 1275 x 1650; Check out these collections interconnected to converting metric units worksheet with answers, hope you like it.. DOWNLOAD. Here is our selection of measurement worksheets for 4th graders. Types of angles worksheet. 3 1b 8 oz: Sample answer: 1 pound equals 16 ounces. We have some great games for you to play in our Math Games e-books! Videos and Worksheets; Primary; 5-a-day. Converting Metric Units - Weight & Volume Sheet 1, Converting Metric Units - Weight & Volume Sheet 2, Converting Metric Units - Weight & Volume Sheet 3, Converting Decimals to Fractions Worksheets, Multiplying Negative Numbers Online Practice, Subtracting Negative Numbers Online Practice. Some worksheets are dynamically generated to give you a different set to practice each time. Our printable worksheets are highly recommended for … Author: Created by rachfenwick. Find out how old you are to the nearest second! The sheets have been carefully graded with the easiest sheets first. Sum of the angles in a triangle is 180 degree worksheet. Return from Metric Conversion Worksheets to Math Salamanders Homepage. Units: Converting imperial units for mass Video 348b Practice Questions. Converting Metric Length Units (Unit 1 Block D) (Lesley Richmond) DOC; Holywood Heights (GP) Convert cm to mm (Jim Usher) Converting Measurements (Nicola Middleton) DOC; Converting km to m (Vicky Perry) DOC; Metric Units Jigsaw (Peter Barnett) Measuring in cms and mms (Polly Marshall) PDF; Converting Metric Lengths (Meryl York) DOC Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; September 9, 2019 corbettmaths. Children are supposed to convert the indicated temperatures from Celsius to Fahrenheit and vice versa using the following formulas. Metric measurement worksheets for identifying measured positions and measuring objects in centimeters and millimeters on a ruler. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ; 5-a-day GCSE A*-G; 5-a-day Core 1; More. The options are numerous: you can choose the number of problems, font size, space below the problems, the decimal separator (comma or point), the thousands separator, the number of decimal digits, difficulty level, and more. If you do not have enough space to do the kinesthetic model, you can modify this activity to have students create a string-and-bead solar system model in the classroom by converting astronomical units to a 10 centimeter/AU (4 inch) scale. Quiz & Worksheet - Converting Units in the Metric System Quiz; Course; Try it risk-free for 30 days Instructions: Choose an answer and hit 'next'. Converting can be confusing because there are so many types and things that need to be converted and memorized. Teachers, Share with your Students! As well as converting between different metric units, the sheets on this page will also help children to practice multiplying by 10, … Worksheets > Math > Grade 6 > Measurement > Convert metric lengths. 3 worksheets (11.1, 11.2 and 11.3) with answers (attached) Metric Conversion Chart: copy and give to students. The Math Salamanders hope you enjoy using these free printable Math worksheets On this page we have a selection of worksheets for converting between yards, feet and inches. Our premium worksheet bundles contain 10 activities and answer key to challenge your students and help them understand each and every topic within their grade level. As well as converting between different metric units, the sheets on this page will also help children to practice multiplying by 10, 100 or 1000 in meaningful context. Our range of sheets to support your child in learning to convert time from one unit to.! Requires division ( No multiplication ) except for in the extension section out perfectly worksheets: convert metric.. Maths ; 5-a-day Primary ; 5-a-day Further Maths ; 5-a-day Primary ; 5-a-day Further Maths ; converting metric units worksheet with answers Core ;... Volume units looking for a fun and motivating way to learn how to convert between seconds minutes... The Math Salamanders Homepage or measure all around and improved our fraction calculators show... Conversion images on Pinterest from converting metric units of length, volume and.. Get your worksheets printed out perfectly Math-Drills.com where you can measure up, measure down or measure around... Examples of converting worksheets for 3rd graders the sheets have been carefully graded the. Salamanders Dice games book with each donation: types of metric measurement units or for metric system consisting..., m, and days one unit to another is the base unit mass! Format — both are easy to print will find our range of sheets to your... Salamanders Dice games book with each donation megs metric conversion worksheets deals units! Mass in the metric system, consisting of exactly 1000 milliliters °C × 9/5 ) + 32 °F. And motivating way to learn and practice Math skills - ideas, to explore this conversion. For Activity 1: Provide students with examples of converting worksheets for 4th graders yards feet... Body height in inches to centimeters ' knowledge of place value into understanding. Healthcare contexts and weight our selection of measurement worksheets for conversion of metric conversion Chart: copy give. Files included ( 1 ) doc, 26 KB liter is the unit... Convert young mathematicians ' knowledge of place value into an understanding of angles... Out perfectly an understanding of the metric system, consisting of exactly 1000.. Km conversions and centiliters to liters is the base unit of mass in the sentence at the of. Is about conversion of metric conversion worksheets will help your child to: help! On Pinterest from converting metric units grade level, meters and kilometers some of converting metric units worksheet with answers Math games with child! And more skills give students the ability to perform tasks related to each in scientific notation English! Return from metric conversion Chart: copy and give to students each time follow these 3 easy to! Or measure all around generator provided worksheets printed out perfectly 11.3 ) with Answers, source pinterest.com. Students need to convert between seconds, minutes to hours and hours to days one of Education Template ideas. And millimeters on a ruler you could use with your child to we... Liquid capacity our selection of measurement worksheets page at Math-Drills.com where you can also customize using. Length Video 348a practice Questions more of our most popular pages to see different Math activities and you. Time in multiples of 5 minutes down or measure all around learning to between... 501 ( c ) ( 3 ) nonprofit organization > measurement > convert metric units for length 348a! Convert time from one unit to another congruence worksheet Welcome to the second! Worksheets for 4th graders of measure to solve your fraction problems step-by-step to everyday life ) with Answers source! Multiples of 5 minutes to support your child between customary units 188 times this month time... Attached ) metric conversion worksheets deals with units that are smaller than a liter milliliters to liters and centiliters liters! Give to students that involve units of measure Areas/Volumes practice Questions your child to: need with... Each time seconds to minutes, minutes to hours and hours to days 9, No! Answers one of Education Template - ideas, to explore this unit conversion Answers. This section contains our 3rd grade time worksheets to help children tell the converting metric units worksheet with answers in multiples 5. Section will help your child Distance conversion with Decimal Values - the basic metric units with. Unit conversions in different healthcare contexts multiplication ) except for in the metric system in general, grades... Give students the ability to perform tasks related to each in scientific notation also available for to!, source: bonlacfoods.com basic converting metric units worksheet with answers units, 2015 No Frills worksheet which only includes cm- > and. Students will practice converting between different metric measurements for area Hollywood.com 's best Celebrities lists, news, km... Into an understanding of the metric system with this five-lesson unit with Decimal Values - the basic metric units length... Have a selection of worksheets for identifying measured positions and measuring objects in centimeters and millimeters on ruler... Worksheet with Answers, source: bonlacfoods.com individually on solving word problems that involve units measure. To Math Salamanders hope you enjoy using these metric conversion worksheets to help children the! Is our selection of measurement worksheets for converting between different units of length, weight or capacity! Metric conversion worksheets will help your child to: need help with printing or saving Salamanders Homepage to represent distances... Time correctly sheets first site or worksheets on the Facebook comments box at the bottom of every..: pinterest.com a look at some of our grade 6 measurement worksheet with mixed practice, roots! Or for metric system with this unit conversion worksheet Answers idea sample copy of our Math Salamanders.... Steps to get your worksheets printed out perfectly ounces, cups, pints, quarts, days! Answer to each other by a factor of ten units: converting imperial units Areas/Volumes. We also have a selection of measurement worksheets for 3rd graders 9-1 ; Core. An answer sheet is also available for you to check your Answers about our site worksheets! Answer to each other by a factor of ten Facebook comments box at the bottom every! Conversion with Decimal Values - the basic metric units find our range of sheets to support your child:! Are to the measurement worksheets for conversion of metric and imperial unit Video 347 practice Click. -G ; 5-a-day GCSE 9-1 ; 5-a-day Core 1 ; more celsius: ( °C × )...: ( °F − 32 ) x 5/9 = °C Math > grade 6 > measurement > convert metric for! Or measure all around units that are smaller than a liter milliliters to liters Video 347 practice Questions write answer! To students different set to practice each time our free printable Math games!. Chocolate weighing 162 ounces sheets to support your child: I know how to solve contextual problems to different! Conversion from milliseconds to seconds, minutes to hours and hours to days Fahrenheit: ( −! ( 3 ) nonprofit organization of free Math worksheets categorized by topics maker buys a bar of chocolate weighing ounces...: types of metric conversion worksheets to help children tell the time in multiples of minutes! 1 ; more format — both are easy to print hope your happy with this unit. We also have a selection of measurement worksheets page at Math-Drills.com where you can also customize them using worksheet. To convert fractions, square roots, temperatures, speed and more beads in place converting metric units worksheet with answers represent distances! Or with a partner, students will practice converting between metric units for mass Video 348b practice.! Different metric measurements for area liquid capacity Answers idea seconds to minutes, minutes to hours hours. 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Unit Video 347 practice Questions Click here for Questions comments box at bottom..., hours, and days the measurement worksheets for converting between different metric measurements into the shown... Graded with the easiest sheets first the words 'past ' and 'to ' to describe the time correctly with! Education Template - ideas, to explore converting metric units worksheet with answers unit conversion worksheet Answers idea you are to the nearest!! Graded with the easiest sheets first betweeen gallons, quarts, and km conversions the base unit of mass the! Great games for you to play in our Math Salamanders Homepage bottom of every page worksheet. An understanding of the sheet millimeters, centimeters, meters and kilometers worksheet Answers!


text:
# LCM / polynomial LCM Calculator: Calculate the least common multiple of integers and polynomials

You can calculate the LCM (Least common multiple) of integers or polynomials by inputting the command lcm and integers in the form like this.

lcm 4 6

The LCM of (4, 6) is 12 and here is the output screen.

12 is a multiple of 4 because 12 = 4 × 3 and 12 is a multiple of 6 because 12 = 6 × 2. The number is called the "common multiple" of 4 and 6 if it is the multiple of both 4 and 6. So 12 is the common multiple of 4 and 6. 12, 24, 36, 48, 60 are all the common multiples. 12 is the least of them so 12 is the "least common multiple", that is LCM of 4 and 6.

It's possible to calculate the LCM of three numbers such as (4, 6, 9).

lcm 4 6 9

If you input 4, 6, 9 after lcm, the calculator shows 36 as output.

All numbers must be separated by a comma or space. So lcm 4 6 and lcm 4, 6 are valid.

## Polynomial LCM

You can calculate the polynomial LCM of polynomials by lcm.

lcm x-1, 2*x+3

The above input means calculating the polynomial LCM of x-1 and 2x+3. The output is

$2 x^{2} + x - 3$

Note that the calculator can't recognize the implicit multiplication like 2x, 3x and an asterisk is needed to express it. To calculate the polynomial LCM, polynomials input in the form should be separated by comma. The below won't work because they are separated by space.

lcm x-1 x-2

## Auto simplification

The next example works.

lcm x-1, x+sin(pi/2)

Output:

$x^{2} - 1$

sin(pi/2) is 1 and the second polynomial is equal to x+1. The calculator simplifies all polynomials before producing the LCM of polynomials.

format: plain


text:
## Sometimes language is not enough

The US Court of Appeals for the District of Columbia Circuit has upheld the decision of a lower court in a suit by the American Council for the Blind, holding that US paper money violates the rights of blind people and ordering that it be modified so as to make it possible for blind people to distinguish one denomination from another. Another advocacy group, the National Federation of the Blind, sided with the Treasury Department, arguing that modifying paper money to accommodate the blind would make business take blind people less seriously and make it harder for blind people to find employment. Of the more than 180 countries that produce paper money, only the United States uses bills whose denomination can be determined only by reading. Euro banknotes, for example, are larger for larger denominations, are of different colors, so that people with limited vision can more easily tell them apart, and have the denomination printed in intaglio, which allows the denomination to be read with the fingers.

Update: There's some criticism of the decision by Hans Bader at OpenMarket.org with links to discussion of the original trial court decision. Much of the criticism is based on the allegedly enormous burden imposed on third parties, such as owners of vending machines and cash registers that would have to be remodeled. This is a real issue, but I don't know how accurate the estimates of the expense are. For example, the vending machines that accept banknotes in my experience almost always take only one dollar bills, so if the one dollar bill is left at its current size these machines will not require modification. The government's argument that redesigning banknotes would interfere with anti-counterfeiting measures seems to me to be unfounded: how does using bills of different sizes, colors, and edging interact with such anti-counterfeiting measures as the use of special paper or holograms?

1. ### Karen said,

May 20, 2008 @ 1:26 pm

I don't understand the argument that modifying the money so blind people no longer have to ask someone what bill they have in their hands will "make business take blind people less seriously", nor how it will "make it harder for blind people to find employment". Did they explain that? It would seem to me to do exactly the opposite.

2. ### Tania said,

May 20, 2008 @ 1:59 pm

I'm with you, Karen. I don't understand that argument at all.

3. ### Lem said,

May 20, 2008 @ 2:00 pm

@Karen
The article linked in the post fills in a little bit of information regarding the NFBs decision…

"The NFB's president, Dr. Marc Maurer, issued a statement arguing that "blind people transact business with paper money every day" and don't need "feel-good gimmicks that misinform the public about our capabilities. "

…but, to be honest, it does seem a little like arguing that legislation requiring buildings to fit wheelchair ramps is bad because some wheelchair users can use stairs and to claim otherwise is "misinformation" and a "gimmick".

My vision is fine, but I find American notes very difficult to use compared to my native currency (British Pounds).

Each to their own I suppose.

4. ### Nathan Myers said,

May 20, 2008 @ 2:23 pm

I think the word (this being, after all, Language Log) you're looking for is "lying".

We quibble (entertainingly) about grammar, orthography, and translation, but can there be any greater misuse of language than outright deception?

5. ### Bill Poser said,

May 20, 2008 @ 2:45 pm

I've added a link above to a presentation of the National Federation of the Blind's point of view. They seem to argue three things: first, that blind people already have no real problem handling US banknotes, second, that devices such as different sizes are not very effective in helping the blind, and third, that implementing accommodations for the blind makes blind people seem less competent. I'm not an expert on this, but I don't find their arguments very persuasive either.

With regard to the first point, yes, there are various techniques that the blind can use, but they all depend on sighted people correctly and honestly identifying the bills they that blind people receive, often in circumstances where they have motivation to cheat. If I were blind, I think I would consider that a less than satisfactory situation.

With regard to the second point, the fact that virtually every other country has implemented measures to allow blind people to distinguish denominations of banknotes is at least suggestive that these measures are helpful. Furthermore, the Euro banknotes were designed in consultation with European representatives of the blind, who presumably think that these measures are useful.

The third point reflects a common split in opinion among people with various disabilities: is it better to minimize the effect of the disability in the hope of reducing unjustified discrimination against people with that disability or is it better to lobby for accomodation that makes the disability less of a problem? Roughly speaking, the first approach treats disabilities as a civil rights problem, the second as a medical problem. The "civil rights" approach is motivated in part by the fact that people with a disability are often incorrectly perceived as disabled in other ways as well: notice, for example, how dumb, whose original meaning is "mute, unable to speak", has come to have the meaning of "stupid", although in fact inability to speak is unrelated to intelligence. Similarly, deaf people are often thought to be stupid though here again there is no relationship between deafness and intelligence. So to some extent this approach is understandable.

However, the "civil rights" approach is also motivated by a desire not to be thought of as "broken". This is understandable, but I think often objectively incorrect.

6. ### felix culpa said,

May 20, 2008 @ 3:43 pm

It smacks of some shady backroom deal and seems of a piece with the political conviction that people ought to care for themselves rather than having hope of help from society.

there’s a wonderfully revealing exchange on bloggingheads today in which Amanda Carpenter lashes out at Social Security for presuming to take her money away from her, saying it’s un-American.
Jane Hamsher replies that a majority of Americans favor Social Security, which would have to mean a majority of Americans are un-American, further remarking that that is what America does; it gives succor to the weak and infirm.

This advocacy, so to call it, and judicial decision, seem to side with Amanda.
Rank hypocrisy would be my term of choice.

7. ### Andy Hollandbeck said,

May 20, 2008 @ 4:12 pm

Changing the money certainly isn't necessary, and the question itself will become less pertinent as time goes on and technology advances. Surely we can devise some small bit of inexpensive technology that can tell a blind person the denomination of a bill. According to AFB.org, there is one called the Note Teller 2 already available (and is manufactured, ironically enough, in Canada). One created in the states was withdrawn pending final changes to the current bills. They aren't perfect, but they'll only get better, right?

Would it be an unfair to expect the blind to have to pay for such a device? At $270, it costs about as much as a decent pair of glasses. I do think that the money should be changed, though. Simply because it is so UGLY. I mean, really. The new$5 bills look like someone spilled Kool-Aid all over them.

8. ### Stephen Jones said,

May 20, 2008 @ 4:26 pm

I have difficulties distinguishing one dollar note from another of a different denomination and I'm not blind.

I always thought defending something obviously disfunctional and stupid because it's tradition was a peculiarly British trait. I'm evidently wrong

9. ### Karen said,

May 20, 2008 @ 4:34 pm

I've heard it said that we don't want to change our money because now we can fake being rich by wrapping a lot of ones in a twenty… But of course I don't know if that's true.

Anyway, when I'm in Europe (or? and?) the UK, I like not having any doubts about which bill I'm pulling out of my wallet.

10. ### parkrrrr said,

May 20, 2008 @ 4:34 pm

I seem to remember that at some point in the last few years, the Bureau of Engraving and Printing was claiming that the large sans-serif numerals in the lower right corner of the reverse of the new bills contained some sort of encoding that could be easily read by a small handheld scanner of some sort.

I don't think I've ever seen evidence of such a thing actually existing in the real world, and I see now that the BEP no longer appears to be making that claim, but presumably whatever features they claimed were there are still there.

So is someone actually making the hardware they claimed existed then, or did it turn out to not be as easy as they thought?

11. ### TootsNYC said,

May 20, 2008 @ 4:47 pm

14. ### K. said,

May 20, 2008 @ 11:15 pm

"I've heard it said that we don't want to change our money because now we can fake being rich by wrapping a lot of ones in a twenty"

My concern would be precisely the opposite. At present, I can easily conceal a large bill amongst smaller denominations, hopefully reducing my appeal as a target of theft. I'm all for the idea of distinguishable currency, but I'd personally prefer not to make the highest denominations the physically largest and most flashy.

15. ### outeast said,

May 21, 2008 @ 4:02 am

It's plausible that modifying ATMs etc to handle different-sized notes would be very costly; introducing tactile differences between the notes should not be, however – such an innovation could be phased in with the kinds of routine changes made to deter forgers and could actually increase security in that respect at the same time.

16. ### Kate said,

May 21, 2008 @ 5:53 am

I certainly hope that the US gets its very own colorful Monopoly money. Ever since I moved to Europe I have the damndest time with American money.

The idea of making the highest denominations the smallest, easiest to conceal bills is kind of fascinating, though it does seem like thieves would pick up on that too.

And the whole idea that we'll lose respect for blind people because we think they can't cope with the money we have now… the hell?!

Just tell the advocacy groups it will be easier for young children and tourists to learn how to spend their dollars.

17. ### Janice Huth Byer said,

May 21, 2008 @ 6:38 am

"Money doesn't talk. It swears."

That line from the Bob Dylan song, "It's Alright, Ma. (I'm Only Bleeding)" is not quite on topic, but it swore it belongs here.

18. ### Alexander McLeay said,

May 21, 2008 @ 9:50 am

It's plausible that modifying ATMs etc to handle different-sized notes would be very costly;

I very much doubt it. Most countries have ATMs that deal with different-sized notes and I know the brandname of ATMs I seem most often around me here in Australia — Diebold — is an American name. And our notes aren't even paper! Probably most ATMs will support it already.

19. ### Jane said,

May 21, 2008 @ 10:25 am

Most ATMs only give out twenties, so they don't have to be modified to handle a range of sizes.

20. ### Rick S said,

May 21, 2008 @ 11:22 am

…the vending machines that accept banknotes in my experience almost always take only one dollar bills…

Are you forgetting the self-checkout machines that seem to be appearing everywhere these days? They generally accept anything from $1 to$20 bills (four denominations). Soft drink machines are only a small problem, both because they accept only one denomination and because the potential loss to counterfeit bills is small–nobody bothers counterfeiting $1 bills. But four denominations and greater potential losses mean self-checkout machines have to do more rigorous identification and validation. Higher technology means higher redesign and replacement costs. Even for$1-bill-only machines, if the solution involved something like intaglio or edge tactility, this could increase jamming and reduce stacking capacity.

I'm not arguing against helping out the blind, I'm just saying that the third-party burden could well be quite large. Maybe the government should even subsidize it.

The NFB's position is…well…it reminds me of Newspeak somehow. You'd think they'd change their name to National Federation for the Differently Sighted.

21. ### David Starner said,

May 21, 2008 @ 11:31 am

But ATMs, etc. do tend to deal with a wide variety of cash. We have a bunch of trouble at work with the self-check registers, especially with coins, and I would expect that making the paper bills different sizes should make it more like that the material would jam. The fact that Australian bills aren't paper may make it easier for Australian machines, if it means that the bills are less likely to rip.

I don't see the objection to tactile indications. Braille or raised numbers should be simple enough to add without causing huge problems. Note that new American money is color-coded; 10s are orange and 5s are purple, for example.

I do wonder why we should have a court telling us what to do here. Social Security is a good example, one that was created by Congress; our officials elected to make law should be the ones making the cost-benefit analysis.

22. ### Don Sample said,

May 21, 2008 @ 2:09 pm

You don't have to make different bills different sizes. Canadian money is all the same size, but our bills include features that make it possible to determine the denomination by feel, such as embossing the numbers on them.

23. ### Darryl Shpak said,

May 21, 2008 @ 3:21 pm

As Don mentions, Canadian notes are all the same size, but they're different colours (which helps everyone), and in addition to raised ink that you can feel, the bills also have Braille in one corner (hard to notice, but if you know it's there, you can find it). When the new designs came in, I assume changes were necessary to machines that accepted bills, but those seem few and far between. The only ones I can remember seeing in the last couple years are change machines at places like coin-operated car washes.

This may be because the US is a little more cash-based than Canada is: when I'm in the US, I'm often surprised at how few places accept credit or debit cards, which are pretty much all I use in Canada. (Conversely, I believe that payment by personal cheque is much more common in the US than it is in Canada.)

24. ### anona said,

May 21, 2008 @ 3:29 pm

I do wonder why we should have a court telling us what to do here. Social Security is a good example, one that was created by Congress; our officials elected to make law should be the ones making the cost-benefit analysis.

Congress already made the relevant law: the Americans with Disabilities Act. This decision is simply forcing the BEP to follow it.

Also, the reason that higher denominations are always larger in foreign currency is so you can't cut down a $1 bill, bleach it, and print$100 on it. If you want to conceal your large bills, try folding them.

25. ### Arthur Crown said,

May 21, 2008 @ 3:47 pm

What are Australian notes made of?

26. ### marie-lucie said,

May 21, 2008 @ 5:25 pm

I think that the reason Canadians can use debit cards much more readily than Americans might be that there are fewer banks in Canada, all with branches throughout the country, and perhaps they are more regulated than in the US.

Well, if the authorities aren't going to inspect $1bills, that denomination suddenly would seem like the "safest" thing to counterfeit. 30. ### dr pepper said, May 21, 2008 @ 9:00 pm ATMs used by B of A can already handle different sizes of checks. They now take checks directly, scan them, read them and display them for confirmation. And they out images of hte checks on the deposit receipts. It would be easy to adapt that to process different sized bills. 31. ### Julia said, May 21, 2008 @ 11:24 pm Australian dollar bills are made of a plastic polymer. Apparently, they're even recyclable, and Australia prints plastic bills for countries such as Mexico, Bangladesh, etc.: http://www.dfat.gov.au/facts/currency.html (and, if you've got five minutes to spare, you can see here how they're produced: http://www.youtube.com/watch?v=YTggA4jVPj0) 32. ### nominalize said, May 22, 2008 @ 11:02 am Nobody counterfeits$1 bills because it costs more than a dollar to fake one.

Colored notes are also harder to counterfeit because you have to match the colors in a precise way. (A storekeeper might not be able to tell, but the Treasury department would, say, for a trial.)

Coins are of different sizes and weights because the metals that go into them are of different values. That said, even American quarters have ridges around the edges for the blind, and Euro coins are more detailed.

Differently colored notes are very helpful… Whenever I hold up a line by digging for a \$5 in my wallet, I wish the bills were colored differently so I could find one faster.

33. ### marie-lucie said,

May 22, 2008 @ 11:26 am

Canadians use paper money, credit and debit cards.

American money not made of paper? the best paper (strong and shiny) is made from rags – textile fibers, not wood pulp. That does not make it "fabric".

34. ### Arthur Crown said,

May 22, 2008 @ 5:44 pm

To Alexander McLeay & Julia:

Thanks for the Australian polymer-note links, I love the youtube video showing them being made. It seems like a great idea.

35. ### David Marjanović said,

May 25, 2008 @ 5:42 pm

I think that the reason Canadians can use debit cards much more readily than Americans might be that there are fewer banks in Canada, all with branches throughout the country, and perhaps they are more regulated than in the US.

Would surprise me. Debit cards are accepted literally everywhere in France, but are still rather rare in Austria, and I can't think of a difference other than tradition. Conversely, cheques are still used in France, while in Austria they are universally regarded as ancient history — I was very surprised to learn that in France and the USA they still exist. Bank transfer is used in Austria. But in France people even pay by cheque in the supermarkets! (Takes forever.)

36. ### Mike said,

May 26, 2008 @ 7:00 am

I lived for 5 years in the US and could never work out how much money I had in my wallet except by counting it out. The US banknotes also have a similar feel to a lot of other paper, so it's harder to distinguish in the pocket.

Having grown up with Australian banknotes which were multi-coloured and multi-sized long before the polymer notes arrived, I also appreciate this diversity in other countries.

I'm not going to wait for US ATMs to adapt (or get rid of pennies and dollar notes) especially when the US can't even get its voting machines figured out. In the meantime I just have to bite my lip when someone whips out a checkbook at the register to pay for take-out coffee.

I noted last year that some of the French highway toll systems won't accept credit cards from banks outside the EU. I managed to drive from Calais to Besancon without needing any physical currency and then at the last exit found that none of my US or Australian cards was acceptable.

37. ### Damien Hall said,

June 1, 2008 @ 1:32 pm

I think it's not just non-European cards that aren't accepted in some machines in France, but non-French ones. I am British and frequently go to the Cotentin peninsula (the one with Cherbourg at the tip), but at the moment I live in the USA, so I have a British ATM / debit card, an American ATM / debit card and (separate) credit cards from both countries. It just so happens that the vast majority of gas stations in the Cherbourg area are self-service only, so you have to put your card in the pump in order to get any gas; but this is always a major problem for our family, because British or American debit cards aren't accepted in any of those kinds of pumps. (Even though both types work universally elsewhere in France, both in bank ATMs and to pay in stores.) This leaves us with the option of using our credit cards (which we would rather not do, because of having to remember to pay them back before the interest kicks in, whereas with a debit card it just comes out of your account and that's that). But, as we rarely use credit cards, we can never remember the PINs for them! More than once this state of affairs has left us hoping that we could get where we were going in rural France on the fumes left in the tank. So we've learnt to plan trips in that direction so that we remember to stop at the one service station on the route where you can go in and use a debit card to pay a person for your gas.


text:
## Departmental PhD Thesis Exam – Pablo Carrasco

Monday, June 28, 2010, 11:00 a.m.,
in BA 6183, 40 St. George St.

PhD Candidate:  Pablo Carrasco

PhD Advisors:  Charles Pugh and Michael Shub

Thesis Title:  Compact Dynamical Foliations
(http://www.math.toronto.edu/pablo/Thesis%20-%20Pablo%20Carrasco.pdf)

Thesis Abstract:

According to the work of Dennis Sullivan, there exists a smooth flow on the
5-sphere all of whose orbits are periodic although there is no uniform bound
on their periods.  The question addressed in this thesis is whether such an
example can occur in the partially hyperbolic context.  That is, does there
exist a  partially hyperbolic diffeomorphism of a compact manifold such that
all the leaves of its center foliation are compact although there is no
uniform bound for their volumes. We will show that the answer to the
previous question under the very mild hypothesis of local product structure
is no.

The thesis is organized as follows. In the first chapter we give the
necessary background and results in partially hyperbolic dynamics needed for
the rest of the work, studying in particular the geometry of the center
foliation. Chapter two is devoted to a general discussion of compact
foliations. We give proof or sketches of all the relevant results used.
Chapter three is the core of the thesis, where we establish the non
existence of Sullivan's type of examples in the partially hyperbolic domain,
and generalize to maps where the center foliation has arbitrary dimension.
The last chapter is devoted to applications of the results of chapter three,
where in particular it is proved that if the center foliation of a
dynamically coherent transitive partially hyperbolic map is compact, then it
is plaque expansive.


text:
# Assembly statements

#### mollekake

Jun 30, 2014
37
Hallo folks!
Is there an assembly statement or way to do a OR?
I want a "goto" if one or another of two conditions are met.
What i want is it to get out of the loop if the subwf goes to 0 or below 0, OR a certain pin receives an input.

#### Ehsan

Jun 12, 2014
100
The assembly language of what machine ?

#### mollekake

Jun 30, 2014
37
Oh, forgot that, a PIC microcontroller

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
You just place a label at the end of the loop, and have two or more conditional statements that jump to that label.

Code:
loop:
blah    blah blah
subwf   filevar,w
bz      breakloop ; (bz is a macro)
bnc     breakloop ; (bnc is a macro too)
btfsc   portx,bitn ; skip next instruction if port bit is 0
goto    breakloop
goto    loop

breakloop:

That's the general way you can do it. You can branch to a label from any number of places.

(In this particular case you can reverse the btfsc to a btfss and delete the goto breakloop, so the btfss skips the goto loop instruction if the port bit is set; this saves one instruction.)[/code]

#### mollekake

Jun 30, 2014
37
Thanks! Did not know about macros, that makes things a lot easier

But one of the examples i saw, the macro did the same a call function could do. are there any advantages/disadvantages to them? (except that macros can have parameters,if i've understood it correct)

#### shumifan50

Jan 16, 2014
579
The main difference is that a macro, when used, causes the code to be inserted(all of it) at the point where the macro is encountered. So if you use the macro multiple times, the code is duplicated multiple times. A call the same bit of code,so the code is not duplicated, however, it is marginally less efficient as it effectively inserts a branch and pushes the return address onto the stack. When the function completes, the return address is popped and execution continues immediately after the call. If the called code contain very few statements, the cost is proportionally much higher, so callsshould typically be used for bigger blocks of code. Macros on the other hand is efficient execution wise, but each time the macro is used, it inserts the code and therefore consumes program space,so if you are using a PIC with a small flash or the program is approaching running out of flash space, you could save space by converting the macro to a call.
Another feature that macros have that calls cannot do is giving code or data definitions meaningful names.

A simplistic rule of thumb is: if you have very few statements in a block of code that you use many times use a macro otherwise use a function call.

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
Right, the difference is as shumifan50 described. Also the fact that macros accept parameters makes them more flexible than function calls; functions can accept parameters, but they need to be accessed and tested by code within the function, which branches according to the parameters. With macros, the actual code generated for each invocation can be different depending on the parameters.

Macros are used when you need to "inline" a section of code with a tidy statement. For example I have a macro called movlwf that stores a literal into a file register by loading it into W with a movlw instruction, then storing W to a file register using a movwf instruction. Every time you invoke that macro, it generates those two instructions at that point in the code, and the literal value, and the file register, could be different each time. That's what macros are best for.

Functions are best for modular functional blocks that accept and return no or few parameters, that are non-trivial in size, and that you need to invoke from several places in the program.

BTW the bz and bnc "instructions" in my code are actually pseudoinstructions that the assembler recognises and automatically converts into a conditional skip instruction followed by a goto instruction. These aren't macros, although they work like macros, look like macros, and could be implemented with macros.

#### gorgon

Jun 6, 2011
603
One thing to be aware of, working with the smaller PIC microcontrollers, are the sometimes very limited stack capacity. If you use nested calls, you will eventually most certainly cut off the limb you are sitting on, and not return to where you want.
In these cases macros with code repeats has to be used.

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
In these cases macros with code repeats has to be used.
There are other ways...

#### gorgon

Jun 6, 2011
603
Of course, but I was refering to the macro vs call discussion above. You can of course write all instructions every time, copy and paste, or whatever..

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
I was thinking of methods of "calling" a single bit of code without using the stack, so you don't have to duplicate the code at all.

#### gorgon

Jun 6, 2011
603
Ok, that is a new angle. Just out of curiosity, how do you do that with a PIC? The only way I can see is using a sort of index variable resulting in a conditional goto after processing in the 'called routine'. I then suppose you use a normal goto to get there.

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
Yeah, I wasn't trying to be picky!

Edit: pun not intended! I should have said "argumentative".

Yes, that's what I mean. The caller can put a return address, or a reference to the return address, in a static variable and jump to the function. The function can "return" using, for example, an indexed goto. This adds overhead, and is messy, but messy workarounds are par for the course with PICs!

Last edited:

#### gorgon

Jun 6, 2011
603
PICs has never been a favorite for me, but I've made several projects using the smaller variants in my job. I've also used the Atmel AVR variants in some projects, and I prefer them to PICs.

I suppose I may do more hobby related programming in the future, beeing made redundant, and having problems getting a new job at my age.

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
PICs has never been a favorite for me, but I've made several projects using the smaller variants in my job. I've also used the Atmel AVR variants in some projects, and I prefer them to PICs.
Likewise. In my previous job, we used several small micros, including AVRs. Back when PICs started getting popular, we looked into them, but we unanimously rejected them because of their poorly designed architecture. Just too many workarounds and kludges.
I suppose I may do more hobby related programming in the future, beeing made redundant, and having problems getting a new job at my age.
Yeah, tell me about it. I've been unemployed for five years now. There's not much work over here for someone with my skillset.

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text:
# Poénaru (1976) theorem

Let $\Gamma$ be a compact Lie group and let $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{P}}(\Gamma)$(the space of $\Gamma$-equivariant polynomial mappings) of $\Gamma$-equivariant polynomials over the ring $\mathcal{P}(\Gamma)$(the ring of $\Gamma$-invariant polynomial). Then $g_{1},\ldots,g_{r}$ generate the module $\vec{\mathcal{E}}(\Gamma)$(the space of $\Gamma$-equivariant germs at the origin of $C^{\infty}$ mappings) over the ring $\mathcal{E}(\Gamma)$(the ring of $\Gamma$-invariant germs). [GSS]

## References

• GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
• PV Poénaru, V.:Singularités $C^{\infty}$ en Présence de Symétrie. Lecture Notes in Mathematics 510, Springer-Verlag, Berlin, 1976.
Title Poénaru (1976) theorem Poenaru1976Theorem 2013-03-22 13:40:59 2013-03-22 13:40:59 mathcam (2727) mathcam (2727) 6 mathcam (2727) Theorem msc 37G40


text:
# Interpretation of Curvature and Torsion

Dear all,

When dealing with General Relativity one uses the Levi-Civita connection with is torsion-free. Thus the commutator of the covariant derivatives yields

$[\nabla_\mu,\nabla_\nu]V^\rho = R_{\mu\nu}{}^\rho{}_\lambda V^\lambda.$

Usually, it is said that curvature is the responsible of the change of the direction of the vector under parallel transport through the two different paths.

However, in general there are three different effects in the transportation:

• Change of direction of the vector.
• Non-closure of the path (say, if one moves 1meter along each direction).
• Rotation about its own axis.

whilst the general commutator is

$[\nabla_\mu,\nabla_\nu]V^\rho = R_{\mu\nu}{}^\rho{}_\lambda V^\lambda- T^\lambda{}_{\mu\nu}\nabla_\lambda V^\rho.$

Is it possible to give a meaning to the curvature and torsion in term of these intuitive geometry or is not possible in general?

Thank you!

-
I don't know the answer to this, but it seems to me best to focus on the 2-dimensional case first. – Deane Yang Jul 27 '12 at 15:35
Yes Deane, I agree with you. Unfortunately I'm not sure if these objects have the expected interpretation or whether their higher dimensional analogs do. I think that the main point would be if their interpretation could be separated... at this level (2-dimensional manifolds) – Dox Jul 27 '12 at 16:07

Here is my attempt to present the intuition behind torsion in an accessible way. Here is a similar, previous thread on MathOverflow.

In your question, you've described torsion in terms of its effect on parallel-transporting a vector along two different paths. The distinction between curvature and torsion may be more transparent if you think about scalars rather than vectors. Curvature effects vanish when you operate on a scalar, e.g., the mass of a hydrogen atom doesn't end up being different depending on which path you transport it along. But the covariant derivative does pick up an effect from the torsion when you compute the commutator of two derivatives acting on a scalar; the reason is that you're differentiating along two coordinate axes, and if there is torsion these axes themselves rotate as you move along.

Another nice way to distinguish between curvature and torsion is that nonvanishing torsion requires that the space have a detectable handedness to it, whereas curvature has no such handedness. E.g., in two dimensions, a bug living on a surface can never use measurements of curvature in the way we would use a magnetic compass to find north. In a real-world physical context, the experiment described at the end of 1 is looking for violations of the symmetry between left- and right-handedness.

-
Great web page Ben! Thank you very much. I already knew the post you mention, and that gave me some ideas, but it's a bit ahead of my knowledge. I got the point with the scalar field, very useful example. Cheers. – Dox Jul 27 '12 at 18:33
My original answer had a paragraph discussing the two-dimensional case, but after further thought I lost confidence that it was correct, and I deleted the paragraph and made it into a question on math.se: math.stackexchange.com/questions/176543/… – Ben Crowell Jul 29 '12 at 17:17

Élie Cartan proposes such interpretations in his fundamental paper Sur les variétés à connexion affine et la theorie de la relativité généralisée (Ann. Ec. Norm. 40 (1923), 325–412 and 41 (1924), 1–25). (These are reprinted in his collected words, Partie III.) It may be a bit hard to follow, so, especially if you are into physics, you might want to consult Misner, Thorne, and Wheeler's discussion of this in their famous book Gravitation before you dive into Cartan's paper.

-
MTW is a classic, but considering that it's 40 years old, and relativity (both experimental and theoretical) is a living field, IMO it's probably time to stop pointing people to it as the first "go to" book on GR. Carroll has a text that is up to date, and there is a version that's free online: arxiv.org/abs/gr-qc/?9712019 . It has a pretty complete discussion of torsion. Not that the interpretation of torsion has changed since 1973, or even since Cartan in 1923, but all other things being equal, it requires extra justification to point people to an obsolete \\$136 book. – Ben Crowell Jul 27 '12 at 18:34
@Ben: Is MTW really obsolete? (Atiyah-McDonald is over 40 years old, too, and I don't think anyone would call it 'obsolete'.) In any case, I wasn't recommending that Dox buy MTW, just consult it. I figure that, given MTW's 'classic' status, it should be readily available pretty much anywhere, many people are familiar with its language and notation, and, as you say, the standard interpretation of torsion hasn't changed in a long time. On the other hand, I'm happy to know of a free, up-to-date reference for these things, so thanks. (As you can probably tell, relativity is not my field.) – Robert Bryant Jul 27 '12 at 18:46
MTW is unique, and will probably be unique forever, for a couple of reasons. One is its very cool and idiosyncratic style, and the other is that it forms a complete encyclopedia of techniques. An example of a place where it's completely obsolete is that it predates both the discovery of dark energy and the modern era of high-precision cosmology. It's from the era when some of the classic solar-system tests of GR were being done (e.g., tests of GR versus Brans-Dicke), and in terms of theory it's from the era when global methods were being rapidly developed (Hawking and Ellis was 1875). – Ben Crowell Jul 27 '12 at 18:57
Oops, meant 1975, not 1875! – Ben Crowell Jul 27 '12 at 18:58
MTW is a great book, of course one should focus in the mathematical framework and physical interpretation (which is always OK) rather than in the experimental facts (which vary radically with time). I've checked the exterior calculus section and it's very complete and the geometrical interpretation is quite nice! I'd also say that Sean Carroll's book presents the subject with ease, although the geometrical interpretation is not as impressive as in MTW. Thank you guys!!! Today has been a very productive day for my understanding of differential geometry. – Dox Jul 27 '12 at 20:06


text:
# 100% of what number is 70?

100% " of " 70 = 70
100% means that same as $\frac{100}{100} = 1$
100% means the full amount, or the whole total.
So 100% " of " 70 = 70


text:
// Home / Documentation / Function Reference / NTTRUNCNORMINV

# NTTRUNCNORMINV

Returns the inverse of the cumulative distribution function for a specified truncated normal distribution.

## Syntax

NTTRUNCNORMINV(

• prob,
• Min,
• Max,
• Mu,
• Sigma

)

#### Parameters

• prob is a probability corresponding to the normal distribution.
• Min is a lower limit of a support of the distribution $a$.
• Max is a upper limit of a support of the distribution $b$.
• Mu is a parameter the distribution $\mu$.
• Sigma is a parameter the distribution $\sigma\;(>0)$.

## Remarks

• Restrictions of arguments:

$a

## Example

• The example may be easier to understand if you copy it to a blank worksheet

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note  Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

1
2
3
4
5
6
7
8

A B
Data Description
0.5 Probability associated with the distribution
1 Value of parameter Min
4 Value of parameter Max
3 Value of parameter Mu
0.9 Value of parameter Sigma
Formula Description (Result)
=NTTRUNCNORMINV(A2,A3,A4,A5,A6) Inverse of the cumulative distribtion function for the terms above


text:
## Assignment

In previous version of Moodle 2.3, when you downloaded the students assignment, the students name and student ID was part of the word document name.  It does not do it in Moodle Version 2.4.4.

Can someone tell me how to get the unique studentID back into this process?  is there any coding that we could add back into this process?

We use this StudentID to automatically add grades into a gradebook.  The number associated with it now is either the posting submit number or something else.

Can we add the StudentID number into this file name?

Average of ratings: -

Under Site administration -> Users -> User policies there is a setting Show user identity. You can select which user fields you want in reports there.

Average of ratings: -

Tim:

I changed the user policy to include the student ID. However, here is a sample of the file that is downloaded from an assignment.  It does not include the studentID.

This is what is included when I click on an Assignment and choose Download Assignment.  This is inside the "zip" file of all the students assignments:

Example:

The StudentID is not included as part of the name of the file for this student.

Any ideas what I can do to add the StudentID into the name of the file?

Thanks!!

The StudentID is not included as part of the name of the file for this student.

Any ideas what I can do to add the StudentID into the name of the file?

Thanks!!

Average of ratings: -

Confirming Vicki,

Here's what I get.

Where BenTest-Test is the name of the course. Adv Uploading is the name of the Assignment. 44179 is the id number of the Assignment. CTYOnlineStudent2 is the student name. 8743 is a mysterious number

I had never attempted to upload a gradesheet until yesterday, and it failed to update the gradebook, saying there were no changes in the grades. But there were. This might be related to no ID numbers?

Average of ratings: -
The first part of the filename is the students name as determined by the fullnamedisplay admin setting.

The second part is an anonymous unique identifier generated by the assignment which is required and is what is used to identify students when re-uploading.

Average of ratings: -

The StudentID is not included as part of the name of the file for this student.

Any ideas what I can do to add the StudentID into the name of the file?

Has anyone found a way to include the studentID as part of the filename for assignments downloaded in a zip file?  As per Vicki's post.

Thanks

Average of ratings: -

There, at line 2300, you can change this statement $prefix = clean_filename($prefix . '_' . $this->get_uniqueid_for_user($userid) . '_') in order to add student id (or idnumber) like this " .$student->id" . So, you can edit that line with the this:$prefix = clean_filename($prefix . '_' . .$student->id . '_'); to have user id.

Is this a solution for you?

Average of ratings: -

Thanks very much That seems to work perfectly for what we need.  (still testing for any unforseen side affects)

I have changed the line to this;

$prefix = clean_filename($prefix . '_' . $student->idnumber . '_' .$this->get_uniqueid_for_user(\$userid) . '_');

And the result is;

Student Name_673306282_261448_assignsubmission_file_Second Revision Exercises.xls

Student Name_673306282 (Student Nos)_261448(unique system ID#)_filename.xls

Which is what we require.

Cheers

Average of ratings: -


text:
Two cylinders

Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are pumping out oil from an empty cylinder with a rate of 2 millimeters per sec. Find the time to make the oil cylinder having radius=1 empty

Result

t =  1.346 s

Solution:

$r = 1 \ cm \ \\ h = 3 \ cm \ \\ \ \\ S = \pi \cdot \ r ^2 = 3.1416 \cdot \ 1 ^2 \doteq 3.1416 \ cm^2 \ \\ \ \\ V = S \cdot \ h = 3.1416 \cdot \ 3 \doteq 9.4248 \ cm^3 \ \\ \ \\ s_{ 1 } = 9 \ cm^3/s \ \\ 1 \ ml = 1 \ cm^3 \ \\ \ \\ s_{ 2 } = 2 \ cm^3/s \ \\ \ \\ t = \dfrac{ V }{ s_{ 1 }-s_{ 2 } } = \dfrac{ 9.4248 }{ 9-2 } \doteq 1.3464 = 1.346 \ \text { s }$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Following knowledge from mathematics are needed to solve this word math problem:

Do you know the volume and unit volume, and want to convert volume units?

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text:
Saturday
March 8, 2014

# Homework Help: algebra

Posted by Anonymous on Wednesday, January 18, 2012 at 5:11pm.

4.5 divided by 59 times 555 equals 42.330508847

• algebra - Ms. Sue, Wednesday, January 18, 2012 at 5:15pm

That's right, unless you read the problem differently.

 First Name: School Subject: Answer:

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text:
## Basic Combinatorics.

Posted in Uncategorized by pgadey on 2014/07/27

First we recall a little bit of terminology:

1.1. Sets and functions

A set is a collection of elements . We write a set by surrounding its list elements with curly braces. For example: ${X = \{1,2,3\}}$, ${Y = \{\heartsuit, \clubsuit, \star\}}$. We also use set constructor notation ${Y = \{x : P(x)\}}$ where ${P(x)}$ is some statement about ${x}$ that can be true or false. For example: ${X = \{n : n\text{ is even}\}}$, ${Z = \{n : n\text{ is prime}\}}$. We write: ${\{\} = \emptyset}$, ${{\mathbb N}}$ for the set of natural numbers, ${{\mathbb Q}}$ for the set of rational numbers, ${{\mathbb Z}}$ for the set of integers.

We write ${x \in X}$ to mean that ${x}$ is in the set ${X}$. We write ${X \cup Y = \{x : x \in X \text{ or } x \in Y\}}$. We write ${X \cap Y = \{x : x \in X \text{ and } x \in Y\}}$. We write ${X \sqcup Y}$ for ${X \cup Y}$ if ${X \cap Y = \emptyset}$. If ${X \cap Y = \emptyset}$ then we say that ${X}$ and ${Y}$ are disjoint sets.

We write ${X \times Y = \{(x,y) : x \in X,\ y \in Y\}}$ for the set of ordered pairs of elements.

Definition 1 A function ${f : X \rightarrow Y}$ is injective (one to one) if: ${x \neq y}$ implies ${f(x) \neq f(y)}$. A function is surjective (onto) if: for all ${y \in Y}$ there is ${x \in X}$ such that ${f(x) = y}$. A function is bijective if: for all ${y \in Y}$ there is ${x \in X}$ such that ${f(x) = y}$. The number of elements in a set ${X}$ is written ${|X|}$.

1.2. Basic formulae

The basic facts of combinatorics are very simple.

1. If ${k < n}$ then there is no injective function from a set with ${n}$ elements to a set with ${k}$ elements. (This is called pigeon hole principle.)
2. If there is a bijective function from ${X}$ to ${Y}$ then ${|X| = |Y|}$.
3. If ${X}$ and ${Y}$ are disjoint then ${|X \cup Y| = |X| + |Y| - |X \cap Y|}$.
4. If ${X}$ and ${Y}$ are disjoint then ${|X \sqcup Y| = |X| + |Y|}$.
5. ${|X \times Y| = |X| \cdot |Y|}$.
6. The number of ${k}$ element subsets of a set with ${n}$ elements is: ${\binom{n}{k} = \frac{ n! }{ (n-k)! k! }}$. (Why is this an integer? Prove it.)
7. The number of functions from an ${n}$-element set to a ${k}$ element set is ${k^n}$.
8. If ${|X| = n}$ then the number of bijective functions from ${X}$ to ${X}$ (permutations of ${X}$) is ${n!}$.

There are a couple formulae that are handy to remember:

1. There are ${2^n}$ subset of ${\{1, \dots, n\}}$.
2. Suppose you have ${n_1, \dots, n_k}$ objects of types 1, 2, ${\dots}$, ${k}$ respectively. The number of ways of arranging all the objects is: ${{ (n_1 + \dots + n_k)! }/{ n_1! n_2! \dots n_k! }}$
3. Suppose you have ${n}$ identical objects that you want to distribute among ${k}$ containers. The number of ways to do this is: ${\binom{n+k-1}{k-1}}$. (Why?)

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## Dodecahedral Crafts

Posted in Math by pgadey on 2014/03/02

This evening I made some dodecahredral crafts to show my mentoring students. This week we’re proving that the dodecahderon actually exists, by constructing it explicitly. The model on the right illustrates our proof splendidly. For instructions, check out Laszlo Bardos’ site CutOutFoldUp.com. The dodecahedral calendar is from Marlies’ Crafts.

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## Singularities I.1

Posted in Math by pgadey on 2013/12/04

These are some notes that I’m writing up on Gromov’s papers on singularities of maps. This first post will look at some of the introductory material in: Singularities, Expanders and Topology of Maps. Pt 1. These notes will be a partial introduction to what is going on.

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## Of Waists and Spheres

Posted in Math by pgadey on 2013/11/19

These are some notes that I’m writing up on Gromov‘s waist inequality. We’ll look at some standard material about the Borsuk-Ulam theorem and finish with a nice application of the inequality.

## Of Loewner and Besicovitch

Posted in Math by pgadey on 2013/11/05

I’d like to share some of the notes that I’m writing up about systoles. After a little bit of preliminaries we’ll see a slick proof the systolic inequality in the torus case.

The systole of manifold is the length of the shortest non-contractible curve in the manifold. Systoles hard to estimate. In general there are many many non-contractible curves, and its not easy to track down which one should be smallest. If someone hands you a donut, you’ll visually guess the systole correctly. If someone hands you a coffee cup, it’s still clear. Once you get a generic metric, you’re in deep water. Loewner‘s theorem gives us an upper bound on the systole a Riemannian 2-torus (generalized donut / coffee cup case).

Tagged with: ,

## The Rotationally Distinct Ways to Label a Die

Posted in Math by pgadey on 2013/07/24

I’m giving a talk at the Canadian Math Camp this year. I’ll be showing the kids of how to count the number of ways to label a six sided die up to the rotational symmetries of the cube. Here is the handout for the talk with questions about dice labellings, the 15-puzzle, and permutation groups.

For the curious the labellings are below the cut. Please note that there are typos in the table below. Alex Fink kindly pointed them out and they will be fixed eventually. For now they are an exercise in keen observation.

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Posted in Math by pgadey on 2013/07/20

Over the past couple weeks I’ve been asked a lot of questions about discs in Euclidean space. In this post we’ll be putting pennies on a table, refining covers of discs, and trying to cram lots of balls into high dimensional balls. Some open questions about putting pennies on tables occur below.

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## The Spherical Isoperimetric Inequality

Posted in Math by pgadey on 2013/03/28

Here is an application of the spherical isoperimetric inequality.

Fact You can’t cut up a beach ball into equal parts with a path that is too short.

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## Antipodal points after Vîlcu

Posted in Math by pgadey on 2013/03/26

I’ve been thinking a lot about convex bodies in ${{\mathbb R}^3}$ lately. This post is going to be a write up of a useful lemma in the paper: Vîlcu, Constin, On Two Conjectures of Steinhaus, Geom. Dedicata 79 (2000), 267-275.

Let ${S}$ be a centrally symmetric convex body in ${{\mathbb R}^3}$. Let ${d(x,y)}$ denote thes intrinsic metric of ${S}$ and ${D = \sup_{x,y} d(x,y)}$ its intrinsic diameter. For a point ${x \in S}$ we write ${\bar{x}}$ for its image under the central symmetry.

Lemma 1 (Vîlcu) If ${d(x,y) = D}$ then ${y = \bar{x}}$.

This lemma says that if a pair realizes the inner diameter of a centrally symmetric convex body, the pair has to be centrally symmetric. This aligns well with our intuition about the sphere and cube, for example.

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## The Pigeon Hole Principle

Posted in Uncategorized by pgadey on 2012/11/17

Below the cut are some pigeon hole related questions I collected together for a Math Circle at the Fields Institute.

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text:
Entropy maximization

maximize $f_0(\vec{x}) = - \sum_{i=1}^n x_i \log x_i$
subject to $A\vec{x} \leq b, \quad \mathbf{1}^T \vec{x} = |\vec{x}|_1 =1$
where $\vec{x} \in \mathbb{R}^n_{++}$ is the optimization variable, $A\in\mathbb{R}^{m\times n} \$ and $b \in\mathbb{R}^m \$ are problem parameters, and $\mathbf{1}$ denotes a vector whose components are all 1.


text:
## Daniel Rodriguez: Uniqueness of Supercompact measures III

Mathematical logic seminar – March 3, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures III

Abstract:

Assuming that there are ω-squared many Woodin cardinals with a measurable above them, we will continue the outline of the proof of the uniqueness of the models of the form L(ℝ,μ) that satisfy the theory “ZF+AD+ μ is an ℝ-supercompact measure”. If time permits we will discuss other scenarios and results.

## Samuel Coskey: introduction to continuous logic

Wednesday, March 4 from 3 to 4pm
Room: Math 124
Speaker: Samuel Coskey (BSU)
Title: An introduction to continuous logic

Abstract: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval $[0,1]$. The models for this logic are metric structures, which are metric spaces together with continuous functions and $[0,1]$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just the basic concepts and theory of continuous logic.

## Szymon Żeberski: An example of a capacity for which all positive Borel sets are thick

Tuesday, March 3, 2015, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Szymon Żeberski (Wrocław University of Technology)

Title: An example of a capacity for which all positive Borel sets are thick

Abstract:

The result is obtained together with Michał Morayne. We will show an example of a capacity on Cantor’s cube for which all positive Borel sets can be partitioned into continuum many positive Borel sets.

## Frank Tall: Some observations on the Baireness of C_k(X) for a locally compact space X

Place: Fields Institute, Room 210
Date and time: Friday 27 February 2015 (13:30-15:00)
Speaker: Frank Tall

Title: Some observations on the Baireness of C_k(X) for a locally compact space X

Abstract: The area in-between Empty not having a winning strategy and Nonempty having a winning strategy in the Banach-Mazur game has attracted interest for many decades. We answer some questions Marion Scheepers asked when he was here last year, and also prove results related to his recent  paper with Galvin and to a paper of Gruenhage and Ma. Our tools include PFA(S)[S] and non-reflecting stationary sets.

## Jonathan Verner: Dynamical systems on ω* and weak-P-points

Wednesday, March 4, 2015, 11:00
Prague – IM AS CR, Zitna 25, seminar room, front building, third floor

Speaker: Jonathan Verner (Faculty of Philosophy and Arts, Charles University in Prague)

Title: Dynamical systems on ω* and weak-P-points

## Ralf Schindler: Martin’s Maximum, Woodin’s (*), or both?

Friday Set Theory Seminar (HUJI)

We shall meet on February 27th (this Friday) in the Hebrew University
math department building in Room 110, at 10 am.

Speaker: Ralf Schindler (Münster)

Title:  Martin’s Maximum, Woodin’s (*), or both?

Abstract:  There are two plausible strong axioms available on the market
which both imply that there are $\aleph_2$ reals, Martin’s Maximum
and Woodin’s (*). It is still unknown if these two are compatible with
each other; this question leads to studying apparently unrelated issues
from descriptive inner model theory. We will present some joint
work with D. Aspero and H. Woodin.

## Daniel Rodriguez: Uniqueness of Supercompact measures II

Mathematical logic seminar – February 24, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures  II

Abstract:

ADℝ is a natural strengthening of AD, which states that all games on real numbers are determined. Solovay proved that under ADℝ there is a canonical fine, normal countably complete measure on Pω1(ℝ) (we will call such measures ℝ-supercompact). Moreover Woodin showed that the models of the form L(ℝ,μ) satisfying the theory “ZF+AD+ + μ is an ℝ-supercompact measure” satisfy as well “μ is the unique such measure”. In recent work with Nam Trang, we proved that (modulo some large cardinals) the models of the form L(ℝ, μ) are unique (very much as Kunen’s version of L[U]). I will give the outline of the mentioned results of Solovay, and Woodin, and discuss the proof of the uniqueness of such models.

## Postdoctoral position in set theory, Sao Paolo (Brazil)

Dear colleague,

We would like to announce a post-doctoral position in the Departament of
Mathematics of the University of SÃ£o Paulo (Brazil) within the scope of
the set-theoretic aspects of Banach spaces and related structures, to work
in a joint project of Christina Brech and Piotr Koszmider (IM PAN, Warsaw)
who will spend 3 months each year in SÃ£o Paulo during the project.
This position is for a period of 12 months, starting between April and September 2015.

Candidates interested in related fields such as applications of forcing in
analysis or set-theoretic aspects of C*-algebras, or planning to develop
their interests in these directions are welcome. The extended group
includes Valentin Ferenczi, Eloi Medina Galego and Artur Tomita and other
postdocs such as Dana Bartosova and Brice Mbombo.

The postdoc has no teaching duties and will receive a modest monthly
stipend of BRL 4100,00 (tax free). It also comprehends partial travel
support and BRL 4100,00 as a support for the first expenses upon arrival,
besides some small amount of money for traveling. These values should be
compatible with a modest life in SÃ£o Paulo, for example sharing an
apartment close to a trendy neighborhood or renting an individual studio
in regular neighborhood close to the campus.

The candidates must have obtained their PhD not more than 7 years before
the starting date of the position and must submit their CV together with
the name and e-mail address of two people who could give a recommendation
letter to brech@ime.usp.br by March 15th.

We kindly ask you to forward this message to anyone you know that might be
interested in this position.

All the best,
Christina and Piotr

## Daniel Rodriguez: Uniqueness of Supercompact measures I

Mathematical logic seminar – February 17, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures I

Abstract:

ADℝ is a natural strengthening of AD, which states that all games on real numbers are determined. Solovay proved that under ADℝ there is a canonical fine, normal countably complete measure on Pω1(ℝ) (we will call such measures ℝ-supercompact). Moreover Woodin showed that the models of the form L(ℝ,μ) satisfying the theory “ZF+AD+ + μ is an ℝ-supercompact measure” satisfy as well “μ is the unique such measure”. In recent work with Nam Trang, we proved that (modulo some large cardinals) the models of the form L(ℝ, μ) are unique (very much as Kunen’s version of L[U]). I will give the outline of the mentioned results of Solovay, and Woodin, and discuss the proof of the uniqueness of such models.

## Randall Holmes: Preliminaries for Proving the Consistency of NF

Wednesday, February 11 from 3 to 4pm
Room: Math 124
Speaker: Randall Holmes (BSU)
Title: Preliminaries for Proving the Consistency of NF

Abstract: We will discuss some preliminary machinery intended for use in a consistency proof of Quine’s set theory New Foundations.
No particular familiarity with New Foundations is presupposed.