text:
# Difference between revisions of "Using TeX Notation"

Jump to: navigation, search

Note: This page is a work-in-progress. Feedback and suggested improvements are welcome. Please join the discussion on moodle.org or use the page comments.

TeX (/'tɛx/tekh, often pronounced TeK in English) is a very widespread and popular way of representing Mathematics notation using only characters that you can type on a keyboard (see Wikipedia). This makes it a useful format to use in Moodle, since it can be entered anywhere you can type text, from forum posts to quiz questions.

TeX expressions can be entered in multiple ways:

• typing them directly into texts.
• using the Java-based Dragmath editor in Moodle's TinyMCE editor.
• using the HTML-based equation editor in Moodle's Atto editor (since Moodle 2.7).

Afterwards, TeX expressions are rendered into Mathematics notation:

• using the TeX filter in Moodle, which uses a TeX binary installed on the server to convert expressions into .gif images (or if that is not available, it falls back to a simple built-in mimetex binary).
• using the MathJax_filter which identifies TeX expressions and uses the Mathjax JS library to render them in browsers at display time (since Moodle 2.7).
• using other third-party solutions.

As you can imagine, the whole field is not as simple as we would like, especially because there are many flavours of TeX and slight variations between tools.

This page focusses only on using TeX in core Moodle. See the links at the bottom of this page for more information on setting up TeX editors and filters, including other tools from the Moodle community that may be suitable for advanced users.

WARNING: This Wiki environment uses a DIFFERENT TeX renderer to Moodle, especially when it comes to control sequences. For this reason images are sometimes used to represent what it should look like in Moodle. YMMV.

To identify a TeX sequence in your text, surround it with $$markers. To invoke a particular command or control sequence, use the backslash, \. A typical control sequence looks like: $$ x\ =\ \frac{\sqrt{144}}{2}\ \times\ (y\ +\ 12) $$  Fraction and square root. Additional spaces can be placed into the equation using the \ without a trailing character. ## Note When an equation is surrounded by a pair of$$ markers, it is displayed centered on its own line. The $$’s are primitive TeX markers. With LaTeX, it is often recommended to use the pair $and$ to enclose equations, rather than the$$ markers, because the newer syntax checks for mistyped equations and better adjusts vertical spacing. If the TeX Notation filter is activated, which set a LaTeX renderer, the same equation as above is obtained with the following control sequence:

 $x\ =\ \frac{\sqrt{144}}{2}\ \times\ (y\ +\ 12)$

However, if the equation is mistyped, it will be displayed enclosed in a box to signal the mistake and if the equation appears in a new paragraph, the vertical space above the equation will adjust correctly.

## Reserved Characters and Keywords

Most characters and numbers on the keyboard can be used at their default value. As with any computing language, though, there are a set of reserved characters and keywords that are used by the program for its own purposes. TeX Notation is no different, but it does have a very small set of Reserved Characters. This will not be a complete list of reserved characters, but some of these are:

 @ # $% ^ & * ( ) .  To use these characters in an equation just place the \ in front of them like \$ or \%. If you want to use the backslash, just use \backslash. The only exception here seems to be the &, ampersand.

## Superscripts, Subscripts and Roots

Superscripts are recorded using the caret, ^, symbol. An example for a Maths class might be:

 $$4^2 \ \times \ 4^3 \ = 4^5$$
This is a shorthand way of saying:
(4 x 4) x (4 x 4 x 4) = (4 x 4 x 4 x 4 x 4)
or
16 x 64 = 1024.

${\displaystyle 4^{2}\ \times \ 4^{3}\ =4^{5}}$

Subscripts are similar, but use the underscore character.

 $$3x_2 \ \times \ 2x_3$$

${\displaystyle 3x_{2}\ \times \ 2x_{3}}$

This is OK if you want superscripts or subscripts, but square roots are a little different. This uses a control sequence.

 $$\sqrt{64} \ = \ 8$$

${\displaystyle {\sqrt {64}}\ =\ 8}$

You can also take this a little further, but adding in a control character. You may ask a question like:

 $$If \ \sqrt[n]{1024} \ = \ 4, \ what \ is \ the \ value \ of \ n?$$

${\displaystyle If\ {\sqrt[{n}]{1024}}\ =\ 4,\ what\ is\ the\ value\ of\ n?}$

Using these different commands allows you to develop equations like:

 $$The \sqrt{64} \ \times \ 2 \ \times \ 4^3 \ = \ 1024$$

${\displaystyle The{\sqrt {64}}\ \times \ 2\ \times \ 4^{3}\ =\ 1024}$

Superscripts, Subscripts and roots can also be noted in Matrices.

## Fractions

Fractions in TeX are actually simple, as long as you remember the rules.

 $$\frac{numerator}{denominator}$$ which produces ${\displaystyle {\frac {numerator}{denominator}}}$ .

This can be given as:

 ${\displaystyle {\frac {5}{10}}\ is\ equal\ to\ {\frac {1}{2}}}$.

This is entered as:

 $$\frac{5}{10} \ is \ equal \ to \ \frac{1}{2}.$$

With fractions (as with other commands) the curly brackets can be nested so that for example you can implement negative exponents in fractions. As you can see,

 $$\frac {5^{-2}}{3}$$ will produce ${\displaystyle {\frac {5^{-2}}{3}}}$

 $$\left(\frac{3}{4}\right)^{-3}$$ will produce ${\displaystyle \left({\frac {3}{4}}\right)^{-3}}$  and

 $$\frac{3}{4^{-3}}$$ will produce ${\displaystyle {\frac {3}{4^{-3}}}}$

 You likely do not want to use $$\frac{3}{4}^{-3}$$ as it produces ${\displaystyle {\frac {3}{4}}^{-3}}$

You can also use fractions and negative exponents in Matrices.

## Brackets

As students advance through Maths, they come into contact with brackets. Algebraic notation depends heavily on brackets. The usual keyboard values of ( and ) are useful, for example:

  ${\displaystyle d=2\ \times \ (4\ -\ j)}$

This is written as:

 $$d = 2 \ \times \ (4 \ - \ j)$$

Usually, these brackets are enough for most formulae but they will not be in some circumstances. Consider this:

 ${\displaystyle 4x^{3}\ +\ (x\ +\ {\frac {42}{1+x^{4}}})}$

Is OK, but try it this way:

 ${\displaystyle 4x^{3}\ +\ \left(x\ +\ {\frac {42}{1+x^{4}}}\right)}$

This can be achieved by:

 $$4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right)$$

A simple change using the \left( and \right) symbols instead. Note the actual bracket is both named and presented. Brackets are almost essential in Matrices.

## Ellipsis

The Ellipsis is a simple code:

 ${\displaystyle x_{1},\ x_{2},\ \ldots ,\ x_{n}}$

Written like:

 $$x_1, \ x_2, \ \ldots, \ x_n$$

A more practical application could be:

Question:

 "Add together all the numbers from 1 ${\displaystyle \ldots }$ 38.
What is an elegant and simple solution to this problem?
Can you create an algebraic function to explain this solution?
Will your solution work for all numbers?"

Answer: The question uses an even number to demonstrate a mathematical process and generate an algebraic formula.

 Part 1: Part 2. Part 3. ${\displaystyle 1.\ 1\ +\ 38\ =\ 39}$ ${\displaystyle 2.\ 2\ +\ 37\ =\ 39}$ ${\displaystyle 3.\ 3\ +\ 36\ =\ 39}$ ${\displaystyle \ldots }$ ${\displaystyle 19.19\ +\ 20\ =\ 39}$ ${\displaystyle \therefore x\ =\ 39\ \times \ 19}$ ${\displaystyle \therefore x\ =\ 741}$ An algebraic function might read something like: ${\displaystyle t=(1+n)\times n/2}$ Where t = total and n = the last number. The solution is that, using the largest and the smallest numbers, the numbers are added and then multiplied by the number of different combinations to produce the same result adding the first and last numbers. The answer must depend on the number, ${\displaystyle {\frac {n}{2}}}$ being a whole number. Therefore, the solution will not work for an odd range of numbers, only an even range.

## Symbols

These are not all the symbols that may be available in TeX Notation for Moodle, just the ones that I have found to work in Moodle.

 \amalg ${\displaystyle \amalg }$ \cup ${\displaystyle \cup }$ \oplus ${\displaystyle \oplus }$ \times ${\displaystyle \times }$ \ast ${\displaystyle \ast }$ \dagger ${\displaystyle \dagger }$ \oslash ${\displaystyle \oslash }$ \triangleleft ${\displaystyle \triangleleft }$ \bigcirc ${\displaystyle \bigcirc }$ \ddagger ${\displaystyle \ddagger }$ \otimes ${\displaystyle \otimes }$ \triangleright ${\displaystyle \triangleright }$ \bigtriangledown ${\displaystyle \bigtriangledown }$ \diamond ${\displaystyle \diamond }$ \pm ${\displaystyle \pm }$ \odot ${\displaystyle \odot }$ \bigtriangleup ${\displaystyle \bigtriangleup }$ \div ${\displaystyle \div }$ \ominus ${\displaystyle \ominus }$ \wr ${\displaystyle \wr }$ \circ ${\displaystyle \circ }$ \wedge ${\displaystyle \wedge }$ \vee ${\displaystyle \vee }$ \sqcup ${\displaystyle \sqcup }$ \leq ${\displaystyle \leq }$ \geq ${\displaystyle \geq }$ \equiv ${\displaystyle \equiv }$ \prec ${\displaystyle \prec }$ \succ ${\displaystyle \succ }$ \sim ${\displaystyle \sim }$ \perp ${\displaystyle \perp }$ \preceq ${\displaystyle \preceq }$ \succeq ${\displaystyle \succeq }$ \simeq ${\displaystyle \simeq }$ \mid ${\displaystyle \mid }$ \ll ${\displaystyle \ll }$ \gg ${\displaystyle \gg }$ \asymp ${\displaystyle \asymp }$ \parallel ${\displaystyle \parallel }$ \subset ${\displaystyle \subset }$ \supset ${\displaystyle \supset }$ \subseteq ${\displaystyle \subseteq }$ \supseteq ${\displaystyle \supseteq }$ \approx ${\displaystyle \approx }$ \neq ${\displaystyle \neq }$ \ni ${\displaystyle \ni }$ \notin ${\displaystyle \notin }$ \in ${\displaystyle \ni }$ \vdash ${\displaystyle \vdash }$ \dashv ${\displaystyle \dashv }$ \bullet ${\displaystyle \bullet }$ \cdot ${\displaystyle \cdot }$

## Arrows

 \leftarrow ${\displaystyle \leftarrow }$ \longleftarrow ${\displaystyle \longleftarrow }$ \Leftarrow ${\displaystyle \Leftarrow }$ \Longleftarrow ${\displaystyle \Longleftarrow }$ \rightarrow ${\displaystyle \rightarrow }$ \longrightarrow ${\displaystyle \longrightarrow }$ \Rightarrow ${\displaystyle \Rightarrow }$ \Longrightarrow ${\displaystyle \Longrightarrow }$ \uparrow ${\displaystyle \uparrow }$ \Uparrow ${\displaystyle \Uparrow }$ \downarrow ${\displaystyle \downarrow }$ \Downarrow ${\displaystyle \Downarrow }$ \leftrightarrow ${\displaystyle \leftrightarrow }$ \longleftrightarrow ${\displaystyle \longleftrightarrow }$ \updownarrow ${\displaystyle \updownarrow }$ \Updownarrow ${\displaystyle \Updownarrow }$ \Leftrightarrow ${\displaystyle \Leftrightarrow }$ \Longleftrightarrow ${\displaystyle \Longleftrightarrow }$ \leftrightharpoons ${\displaystyle \rightleftharpoons }$ \Im ${\displaystyle \Im }$ \nearrow ${\displaystyle \nearrow }$ \nwarrow ${\displaystyle \nwarrow }$ \swarrow ${\displaystyle \swarrow }$ \searrow ${\displaystyle \searrow }$

## Delimiters and Maths Constructs

NOTE: Most delimiters and constructs need additional parameters for them to appear appropriately.

 \{x ${\displaystyle \{x}$ \} ${\displaystyle x|\}}$ \rangle ${\displaystyle \rangle }$ \langle ${\displaystyle \langle }$ \angle ${\displaystyle \angle }$ \= ${\displaystyle \|}$ \sqrt{ab} ${\displaystyle {\sqrt {ab}}}$ \sqrt[n]{ab} ${\displaystyle {\sqrt[{n}]{ab}}}$ \frac{ab}{cd} ${\displaystyle {\frac {ab}{cd}}}$ \backslash ${\displaystyle \backslash }$ \widehat{ab} ${\displaystyle {\widehat {ab}}}$ \\$ ${\displaystyle \}$ \overline{ab} ${\displaystyle {\overline {ab}}}$ \underline{ab} ${\displaystyle {\underline {ab}}}$ \therefore ${\displaystyle \therefore }$ \ddots ${\displaystyle \ddots }$ \% ${\displaystyle \%}$ \# ${\displaystyle \#}$ \vdots ${\displaystyle \vdots }$ \emptyset ${\displaystyle \emptyset }$

WARNINGS: The & character in LaTeX usually requires a backslash, \. In TeX Notation for Moodle, apparently, it does not. Other packages, AsciiMath, may use it differently again so be careful using it. The copyright character may use the MimeTeX charset, and produces a copyright notice for John Forkosh Associates who provided a lot of the essential packages for the TeX Notation for Moodle, so I understand. I have been, almost reliably, informed that a particular instruction will produce a different notice though .:)

There are also a number of characters that can be used in TeX Notation for Moodle but do not render in this page:

 Larger \left(x and \right) brackets \widetilde{ab} \textdegree or (50)^\circ

## Greek Letters

 ${\displaystyle \alpha }$ \alpha ${\displaystyle \beta }$ \beta ${\displaystyle \gamma }$ \gamma ${\displaystyle \delta }$ \delta ${\displaystyle \epsilon }$ \epsilon ${\displaystyle \zeta }$ \zeta ${\displaystyle \eta }$ \eta ${\displaystyle \theta }$ \theta ${\displaystyle \iota }$ \iota ${\displaystyle \kappa }$ \kappa ${\displaystyle \lambda }$ \lambda ${\displaystyle \mu }$ \mu ${\displaystyle \xi }$ \xi ${\displaystyle \pi }$ \pi ${\displaystyle \rho }$ \rho ${\displaystyle \sigma }$ \sigma ${\displaystyle \tau }$ \tau ${\displaystyle \upsilon }$ \upsilon ${\displaystyle \phi }$ \phi ${\displaystyle \chi }$ \chi ${\displaystyle \psi }$ \psi ${\displaystyle \omega }$ \omega ${\displaystyle \Omega }$ \Omega ${\displaystyle \Theta }$ \Theta ${\displaystyle \Delta }$ \Delta ${\displaystyle \Pi }$ \Pi ${\displaystyle \Phi }$ \Phi ${\displaystyle \Gamma }$ \Gamma ${\displaystyle \Lambda }$ \Lambda ${\displaystyle \Sigma }$ \Sigma ${\displaystyle \Psi }$ \Psi ${\displaystyle \Xi }$ \Xi ${\displaystyle \Upsilon }$ \Upsilon ${\displaystyle \vartheta }$ \vartheta ${\displaystyle \varrho }$ \varrho ${\displaystyle \varphi }$ \varphi ${\displaystyle \varsigma }$ \varsigma

Notable Exceptions

Greek letter omicron (traditionally, mathemeticians don't make much use of omicron due to possible confusion with zero). Simply put, lowercase omicron is an "o" redered as o. But note \omicron may now work with recent TeX implementations including MathJax.

At the time of writing, these Greek capital letters cannot be rendered by TeX Notation in Moodle:

Alpha, Beta, Zeta, Eta, Tau, Chi, Mu, Iota, Kappa and Epsilon.

TeX methematics adopts the convention that lowercase Greek symbols are displayed as italics whereas uppercase Greek symbols are displayed as upright characters. Therefore, the missing Greek capital letters can simply be represented by the \mathrm{ } equivalent

${\displaystyle \mathrm {A,B,Z,H,T,X,M,I,K,E} }$

## Boolean algebra

There are a number of different conventions for representing Boolean (logic) algebra. Common conventions used in computer science and electronics are detailed below:

Negation, NOT, ¬, !, ~,

\lnot, !, \sim, \overline{ }

Conjunction, AND, ∧, ${\displaystyle \cdot }$

\land, \wedge, \cdot

Dysjunction, OR, ∨, +,

\lor, \vee, +

Exclusive dysjunction, XOR ⊻, ⊕

\veebar, \oplus

Equivalence, If and only if, Iff, ≡, ↔, ⇔

 \equiv, \leftrightarrow \iff

Example: two representations of De Morgan's laws:

${\displaystyle A\cdot B={\overline {{\overline {A}}+{\overline {B}}}}}$

## Lines

Warning: Drawing lines in TeX Notation in Moodle is an issue, go to the Using Text Notation for more information. If the line is not noted properly then the parser will try to correctly draw the line but will not successfully complete it. This means that every image that needs be drawn will be drawn until it hits the error. When the error is being converted, it fails, so no subsequent image is drawn. Be careful and make sure your line works BEFORE you move to the next problem or next image.

 a couple of lines $$\red \picture(200){(20,0){ \line(180,0)}{(20,180){\line(180,0}$$ The structure of the picture box is that the \picture(200) provides a square image template. The (20,0) provides the starting coordinates for any line that comes after. In this case the start point is at 20pixels in the x axis and 0 pixels in the y axis. The starting point for all coordinates, 0,0, is the bottom left corner and they run in a clockwise manner. Do not confuse this with arcs. The \line(180,0) determines the length and inclination of the line. In this case, the inclination is 0 and the length is 180px. These are enclosed in braces, all inside one set of braces owned by the \picture() control sequence. The next set of commands are the same, that is, the (20,200) are the coordinates of the next line. The x co-ordinate is the 20, that is the distance to the right from the 0 point. The y co-ordinates is the distance from the bottom of the image. Whereas the first line started and ran on the bottom of the picture frame, the y co-ordinate starts at the 200 pixel mark from the bottom of the image. The line, at 180 pixels long and has no y slope. This creates a spread pair of parallel lines. \picture explained

While this explains the structure of a line, there is a couple of elements that you need to go through to do more with them.

## Squares and Rectangles

Drawing squares and rectangles is similar, but only slightly different.

There should be a square box tool, and there is, but unless it has something inside it, it does not display. It is actually easier to make a square using the \line command.

 This box is constructed using: $$\picture(250){(10,10){\line(0,230)}(10,10){\line(230,0)}(240,10){\line(0,230)}(10,240){\line(230,0)}}$$ It is a 250 pixel square box with a 230 pixel square inside it. This box is different in that is has the equal length indicators that are used in a square. $$\picture(250){(10,10){\line(0,230)} (5,120){\line(10,0)} (10,10){\line(230,0)} (120,5){\line(0,10)} (240,10){\line(0,230)} (235,120){\line(10,0)} (10,240){\line(230,0)} (120,235){\line(0,10)}}$$ The rectangle then becomes the same thing, but with one side shorter. For a portrait canvas it would be: $$\picture(250){(10,10){\line(0,230)}(10,10){\line(150,0)}(160,10){\line(0,230)}(10,240){\line(150,0)}}$$ The rectangle can also produce a landscape shape: $$\picture(250){(10,10){\line(0,160)}(10,10){\line(230,0)}(240,10){\line(0,160)}(10,170){\line(230,0)}}$$

## Controlling Angles

Controlling angles is a little different. They involve a different perception, but not one that is unfamiliar. Consider this:

We have a point from which we want to draw a line that is on an angle. The notation used at this point can be positive, positive or positive, negative or negative, positive or negative, negative. Think of it like a number plane or a graph, using directed numbers. The 0,0 point is in the centre, and we have four quadrants around it that give us one of the previously mentioned results.

 $$\picture(100){(50,50){\line(40,45)}}$$, a positive x and positive y $$\picture(100){(50,50){\line(-40,45)}}$$ a negative x and positive y $$\picture(100){(50,50){\line(-40,-45)}}$$ a negative x and negative y $$\picture(100){(50,50){\line(40,-45)}}$$ a positive x and a negative y

Essentially, what these points boil down to is that anything above the insertion point is a positive on the y axis, anything below is a negative. Anything to the left of the insertion point is a negative while everything to the right is a positive.

 $$\picture(100){(50,50){\line(40,45)}(50,50){\line(-40,45)}(50,50){\line(-40,-45)}(50,50){\line(40,-45)}}$$ The co-ordinate alignment process in TeX is not that good that you can use one set of co-ords as a single starting point for all lines. The layering of each object varies because of the position of the previous object, so each object needs to be exactly placed. This co-ord structure has a great deal of impact on intersecting lines, parallel lines and triangles.

## Intersecting Lines

You can set up an intersecting pair easily enough, using the \picture control sequence.

 $$\picture(200){(10,0){\line(150,150)} (0,130){\line(180,-180)}}$$ The lines that are drawn can be labeled. $$\picture(200){(10,0){\line(150,150)}(0,130){\line(180,-180)} (0,10){A}(0,135){B}(140,0){C}(140,150){D}(62,80){X}}$$ To produce another image. To which you may want to ask the question: $$The \ \angle \ of \ AXB \ is \ 72\textdegree. \ What \ is \ the \ value \ of \ \angle BXD?$$ NOTE: Labeling this image, above-right, turned out to be fairly simple. Offsetting points by a few pixels at the start or end points of the lines proved a successful strategy. The X point proved a little more problematic, and took a number of adjustments before getting it right. Experience here will help. With labels the drawing can become a little more like your traditional geometric drawing, but the devil is in the details. The parallel markers need to be placed properly, and that is where experience really comes into it. On lines that are vertical or horizontal, you can get away with using the > or < directly from the keyboard, or the ${\displaystyle \gg }$ or ${\displaystyle \ll }$ symbols. In either case, you need to position them properly. The code: $$\picture(200){(15,45){\line(170,0)} (15,30){c}(170,28){d}(15,160){\line(170,0)}(15,145){e}(180,143){f}(50,20){\line(110,175)}(58,20){a}(140,185){b}(42,32){\kappa}(53,48){\beta} (150,165){\kappa} (90,38){\gg}(80,153){\gg} }$$

## Lines and Arcs

Combining lines and arcs is a serious challenge actually, on a number of levels. For example lets take an arc from the first page on circles.

 Fairly innocuous of itself, but when we start to add in elements, it changes dramatically. $$\circle(120;90,180)$$ $$\picture(150){(75,75){\circle(120;90,180)}(75,75){\line(-70,0)}(75,75){\line(0,75)}}$$ All elements in this drawing start in the same place. Each is layered, and properly placed on the canvas, and using the same co-ord to start makes it easy to control them. No matter the size of the arc, intersecting lines can all be drawn using the centre co-ords of the arc.

## Triangles

Of all the drawing objects, it is actually triangles that present the most challenge. For example:

 $$\picture(350){(10,10){\line(0,320)}(10,330){\line(330,0)}(10,10){\line(330,320)}}$$ This is a simple triangle, one that allows us to establish a simple set of rules for the sides. The vertical always has an x=0 co-ord and the horizontal always has a y=0 co-ord. In this case with an x value of 330 on the horizontal, and a y value of 320 on the vertical, the hypotenuse should then have a value of x=340, and the y=330, but not so, they actually have an x=330 and a y=320. There is no need to add the starting point co-ords to the x and y values of the line. $$picture(350){(10,10){\line(330,0)}(340,10){\line(0,320)}(340,330){\line(-330,-320)}}$$

This triangle has been developed for a Trigonometry page - but the additional notation should provide insight into how you can use it.

 This is a labeled image, but it has an \fbox in it with its little line. With some effort, it could be replaced with two intersecting short lines. $$\picture(350,150){(25,25){\line(300,0)}(325,25){\line(0,110)}(25,25){\line(300,110)}(309,25){\fbox{\line(5,5)}} (307,98){\theta}(135,75){\beta}(150,5){\alpha}(335,75){\epsilon}}$$

 The triangle shows like: We use the different elements of the triangle to identify those things we need to know about a right-angled triangle. The hypotenuse is always the side that is opposite the right angle. The longest side is always the Hypotenuse. To identify the other elements of the triangle we look for the sign ${\displaystyle \theta }$. ${\displaystyle \Theta }$ is the starting point for naming the other sides. The side that is opposite ${\displaystyle \angle \theta }$ is known as the Opposite. The side that lies alongside ${\displaystyle \angle \theta }$ is known as the Adjacent side. To determine which is which, draw a line that bisects ${\displaystyle \angle \theta }$ and whatever line it crosses is the Opposite side. The code: $$\picture(350,250){(25,25){\line(300,0)}(25,25){\line(0,220)}(25,245){\line(300,-220)}(310,25){\circle(100;135,180)}(20,100){\line(310,-75)} (25,25){\fbox{\line(5,5)}}(25,25){\line(150,150)}(165,140){Hypotenuse}(120,2){Adjacent}(2,80){\rotatebox{90}{Opposite}}(270,40){\theta}}$$

# Matrices

A Matrix is a rectangular array of numbers arranged in rows and columns which can be used to organize numeric information. Matrices can be used to predict trends and outcomes in real situations - i.e. polling.

## A Matrix

A matrix can be written and displayed like

In this case the matrix is constructed using the brackets before creating the array:

 $$M = \left[\begin{array}{ccc} a&b&1 \ c&d&2 \ e&f&3\end{array}\right]$$

The internal structure of the array is generated by the &, ampersand, and the double backslash.

You can also create a grid for the matrix.

 A dashed line A solid line A mixed line $$M = \left[\begin{array}{c.c.c} a&b&1 \ \hdash c&d&2 \ \hdash e&f&3\end{array}\right]$$ c|c} a&b&1 \ \hline c&d&2 \ \hline e&f&3\end{array}\right] $$c} a&b&1 \ \hline c&d&2 \ \hdash e&f&3\end{array}\right]$$

The command sequences here are the {c|c.c} and \hdash and \hline. The pipe, |, and the full stop determine the line type for the vertical line.

Matrices also respond to other TeX Notation commands such as size and colour.

 Colour Size $$\blue M = \left[\begin{array}{c.c.c} a&b&1 \ \hdash c&d&2 \ \hdash e&f&3\end{array}\right]$$ $$\fs7 M = \left[\begin{array}{c.c.c} a&b&1 \ \hdash c&d&2 \ \hdash e&f&3\end{array}\right]$$ $$\fs2 M = \left[\begin{array}{c.c.c} a&b&1 \ \hdash c&d&2 \ \hdash e&f&3\end{array}\right]$$

## Creating equal and unequal matrices

Equal and unequal matrices are simply matrices that either share or not share the same number of rows and columns. To be more precise, equal matrices share the same order and each element in the corresponding positions are equal. Anything else is unequal matrices.

Actually equal and unequal matrices are constructed along similar lines, but have different shapes:

 Equal Matrix An unequal matrix $$\left[\begin{array} a&b&1 \ c&d&2 \ e&f&3\end{array}\right] \ = \ \left[\begin{array} 12&11&z \ 10&9&y \ 8&7&x\end{array}\right]$$ $$\left[\begin{array} a&b \ c&d \ e&f \end{array}\right] \ \neq \ \left[\begin{array} 12&11&z \ 10&9&y \ 8&7&x\end{array}\right]$$

## Labeling a Matrix

Addition and subtraction matrices are similar again, but the presentation is usually very different. The problem comes when trying to mix labels into arrays. The lack of sophistication in the TeX Notation plays against it here.

Moodle allows an easy adoption of tables to make it work though. For example:

 Bill the baker supplies three shops, A, B and C with pies, pasties and sausage rolls.
He is expected to determine the stock levels of those three shops in his estimation of supplies.

It is better to use the Moodle Fullscreen editor for this, to have a better idea of how the end product will look and to take advantage of the additional tools available. Design decisions need occupy our attention for a while. We need a table of five rows and four columns. The first row is a header row, so the label is centred. The next row needs four columns, a blank cell to start and labels A, B and C. The next three rows are divided into two columns, with the labels, pies, pasties and sausage rolls in each row of the first column and the matrix resides in a merged set of columns there. So first the table:

 Insert Table - initial properties Merge Cells Button Advanced Properties You may need to look into the Advanced properties setting of the tables and cells to make this work.

This is the immediate result:

While not a very good look, it can be made better by tweaking the table using the advanced settings and properties buttons and then you can tweak the matrix itself.

## Tweaking the Matrix

Things are not always as they seem, be aware, the "c" does not stand for "column", it actually stands for "centre". The columns are aligned by the letters l, for left, c for centre and r for right.

Each column is spread across 50 pixels, so the value of 50 is entered into the alignment declaration. The plus sign before the value is used to "propogate" or to force the value across the whole matrix, but is not used when wanting to separate only one column.

To set the rows is a little more problematic. The capital letter C sets the vertical alignment to the centre, (B is for baseline, but that does not guarantee that the numbers will appear on the base line, and there does not appear to be any third value). The plus sign and following value sets the height of all rows to the number given. In this I have given it a value of 25 pixels for the entire matrix. If there were four or five rows, the same height requirement is made.

The order things appear is also important. If you change the order of these settings, they will either not work at all, or will not render as you expect them to. If something does not work properly, then check to make sure you have the right order first.

## An Addition Matrix

The rule for performing operations on matrices is that they must be equal matrices. For example, addition matrices look like:

with the results obvious. The code is:

 $$\left[\begin{array}{c+50C+25.c.c} 11&14&12 \ \hdash16&12&22 \ \hdash 14&17&15 \end{array}\right] + \left[\begin{array}{c+50C+25.c.c} 60&60&60 \ \hdash 40&40&30 \ \hdash 30&30&30 \end{array}\right]$$

## A Subtraction Matrix

Similar to an addition matrix in its construction, the subtraction matrix is subject to the same rules of equality.

Using the same essential data, we can calculate the daily sales of each of the shops.

The code is:

 $$\left[\begin{array}{c+50C+25.c.c} 72&95&68 \ \hdash 54&61&65 \ \hdash 48&51&60 \end{array}\right] - \left[\begin{array}{c+50C+25.c.c} 11&14&12 \ \hdash 16&12&22 \ \hdash 14&17&15 \end{array}\right] = \left[\begin{array}{c+50C+25.c.c} 61&81&56 \ \hdash 38&49&43 \ \hdash 34&34&48 \end{array}\right]$$

This code looks more complex than it really is, it is cluttered by the lines and alignment sequences.

## Multiplication Matrices

Different than the addition or subtraction matrices, the multiplication matrix comes in three parts, the row matrix, the column matrix and the answer matrix. This implies it has a different construction methodology.

And the code for this is:

 $$\begin{array} 10&14&16\end{array} \ \left[\begin{array} 45 \\ 61 \\ 19 \end{array}\right] \ = \ \begin{array} 450&854&304\end{array}$$

While different, it is not necessarily more complex. For example a problem like:

 Bill the baker is selling his product to Con the cafe owner, who
wants to make sure his overall prices are profitable for himself.
Con needs to make sure that his average price is providing sufficient
profit to be able to keep the cafes open. Con makes his calculations
on a weekly basis, comparing cost to sale prices.

With the pies, pasties and sausage rolls in that order he applies them to the cost and sale price columns :

The code for this is:

 $$\left[\begin{array} 350&310&270 \end{array}\right] \ \left[\begin{array} \2.10&\3.60 \ \2.05&\3.60 \ \1.90&\3.10 \end{array} \right] \ = \ \left[\begin{array} \735.00&\1260.00 \ \635.50&\1116.00 \ \513.00&\837.00 \end{array}\right]$$


text:
Sunday, September 18, 2011 ... /////

The Dutch plan to build a mountain

A few weeks ago, Thijs Zonneveld, a young journalist and former professional bicyclist, revealed that he had always been frustrated by his country's flatness. His sentiment is apparently shared by millions of people in the Netherlands who feel just like a physically oriented, self-watching woman who is not busty.

When he was a kid, Zonneveld would be drawing extra hills on the maps of Holland whose highest mountain, peak, or bump, Vaalserberg, about 323 meters above the sea level, is lower than many hills on the territory of Pilsen. ;-) In an interview, he was dreaming about a man-made mountain that could be used by alpine skiers, bikers, and many others.

Mr Zonneveld originally thought that what he said was just a joke. But his flat nation that got excited abruptly has proved him wrong: it wasn't a joke what you said, Mr Zonneveld, it was damn serious and ingenious, too! And Mr Zonneveld already agrees: I was being serious and ingenious, indeed.

So the result is that hundreds of top Dutch construction and engineering companies began to work on their project to build a 2,000-meter-tall anthropogenic mountain on the Dutch territory. :-)

See Wired and others.

The planned budget is about $0.4 trillion dollars, roughly 1/2 of the Dutch annual GDP. The Swiss are already nervous about the artificial Alp(s) because they could lose the Dutch tourists so they have filled the Netherlands with billboards arguing that the original is always better: the Swiss mountains are as tall as the flat Holland is beautiful. ;-) While building a man-made mountain which requires to lift lots of material to those 2,000 meters, the Dutch could also use their countrymate's ingenious insight that gravity is not a fundamental force; instead, gravity is just an illusion described by a$50-million crackpot paper about the entropic forces. :-D

Edwin Abbott Abbott was clearly inspired by the Netherlands when he wrote his "Flatland".

Make no mistake about it: the 2,000-meter mountain would have to be hollow, a kind of a big building. Otherwise you would need dozens of cubic kilometers of stuff. Note that a cubic kilometer of water weighs a billion of tons and because the relevant materials would probably be even heavier, the Dutch friends would need hundreds of billions of tons of stuff. Homework: compute the potential energy of this mountain and the price of this energy when interpreted as electricity. Because the height of the biggest pyramid in Egypt is just 138 meters or so, the Dutch mountain would have a volume that is 14.5 cubed times i.e. 3,000 times greater than the pyramid which is pretty ambitious.

However, it doesn't look "immediately impossible" to build a hollow construction that just covers a big area, has lots of slopes, and so on. I guess that it could be as easy or as hard as to build a 2,000-meter-tall building with chutes around it. But it might be cheaper for them to buy one such a mountain e.g. in Czechia or Slovakia. For example, Ďumbier, the highest peak in the Low Tatras (Slovakia), has elevation of 2,043 meters which is about what they need. The new Dutch peak, Van Het Nieuwe De 't Ďumbierhaven Huisen, might be cheaper than $0.4 trillion. Even during the Luxembourg Dynasty's reign in the 14th century, the Czech Kingdom didn't quite reach the sea. You have to go to the late 13th and early 14th century to see Czech kings who controlled huge lands from the Adriatic Sea to the Baltic Sea. Of course, I am just trying to discourage the Dutch engineers from building a wonder of the postmodern world. In reality, I am already working on an artificial Czech Ocean which could start on the Czech-Austrian borders. The Czech Kingdom hasn't had access to the ocean for 700 years or so and I've been always drawing seas around our territory. Europe and Palestine Speaking of the Netherlands, it's one of the four EU countries that will probably vote against a segregation of a new Palestinian state within Israel's territory. The Dutch share this opinion with Germany, Italy, and Czechia. Czechoslovakia has always had good relationships with Israel but in the late 1980s, we still had a special period in which the Palestinian officials were our ultimate comrades. ;-) On this picture from October 18th, 1989, exactly 30 days before the Velvet Revolution, Yasser Arafat in between the communist boss Milouš Jakeš (left) and President Gustáv Husák (right) – the two top Czechoslovak jobs were split since 1987 – are smiling because they just gave the highest Order of the Double-Tailed Lion to Arafat. In the 1970s and 1980s, Czechoslovakia exported a huge amount of machinery and weapons to Syria. Syria's debt to Czechoslovakia reached$0.9 billion or so: Syria was among the Czechoslovakia's top debtors. Only relatively recently, we managed to force the Assad dynasty to repay the debt.

format: plain


text:
# Algorithm to find Minimum Distance Between BST (binary search tree) Nodes

2.58K views
0

Given a Binary Search Tree (BST) with the root node root, return the minimum difference between the values of any two different nodes in the tree.

Example :

Input: root = [4,2,6,1,3,null,null]

Output: 1

Explanation:

Note that root is a TreeNode object, not an array.

The given tree [4,2,6,1,3,null,null] is represented by the following diagram:

4

/   \

2      6

/ \

1   3

while the minimum difference in this tree is 1, it occurs between node 1 and node 2, also between node 3 and node 2.

Note:

1. The size of the BST will be between 2 and 100.
2. The BST is always valid, each node’s value is an integer, and each node’s value is different.

0
• Traverse the tree using tree traversal algorithm for e.g. inorder
• Push all the traversed nodes in an array.
• Sort the array
• Find the minimum difference between array elements by looping through

Javascript code below:-

/**
* Definition for a binary tree node.
* function TreeNode(val) {
*     this.val = val;
*     this.left = this.right = null;
* }
*/
/**
* @param {TreeNode} root
* @return {number}
*/
var minDiffInBST = function(root) {
var arr = [];
inorder(root, arr);
arr.sort((a,b)=>a-b);
var minDiff = Number.MAX_SAFE_INTEGER;
var result = [];
var map = {};
for (var i = 0; i < arr.length; i++) {
if (typeof map[arr[i]] === 'undefined') {
map[arr[i]] = arr[i];
}
if (i < arr.length - 1 && Math.abs(arr[i+1] - arr[i]) < minDiff) {
minDiff = arr[i+1] - arr[i];
}
}
return minDiff;
};
var inorder = function(root, arr) {
if (root) {
inorder(root.left, arr);
arr.push(root.val);
inorder(root.right, arr);
}
}

Changed status to publish


text:
The create_informant() function creates an informant object, which is used in an information management workflow. The overall aim of this workflow is to record, collect, and generate useful information on data tables. We can supply as information that is useful for describing a particular data table. The informant object created by the create_informant() function takes information-focused functions: info_columns(), info_tabular(), info_section(), and info_snippet().

The info_*() series of functions allows for a progressive build up of information about the target table. The info_columns() and info_tabular() functions facilitate the entry of info text that concerns the table columns and the table proper; the info_section() function allows for the creation of arbitrary sections that can have multiple subsections full of additional info text. The system allows for dynamic values culled from the target table by way of info_snippet(), for getting named text extracts from queries, and the use of {<snippet_name>} in the info text. To make the use of info_snippet() more convenient for common queries, a set of snip_*() functions are provided in the package (snip_list(), snip_stats(), snip_lowest(), and snip_highest()) though you are free to use your own expressions.

Because snippets need to query the target table to return fragments of info text, the incorporate() function needs to be used to initiate this action. This is also necessary for the informant to update other metadata elements such as row and column counts. Once the incorporation process is complete, snippets and other metadata will be updated. Calling the informant itself will result in a reporting table. This reporting can also be accessed with the get_informant_report() function, where there are more reporting options.

create_informant(
tbl = NULL,
agent = NULL,
tbl_name = NULL,
label = NULL,
lang = NULL,
locale = NULL
)

## Arguments

tbl The input table. This can be a data frame, a tibble, a tbl_dbi object, or a tbl_spark object. Alternatively, a function can be used to read in the input data table with the read_fn argument (in which case, tbl can be NULL). A function that's used for reading in the data. Even if a tbl is provided, this function will be invoked to obtain the data (i.e., the read_fn takes priority). There are two ways to specify a read_fn: (1) using a function (e.g., function() { }) or, (2) with an R formula expression. A pointblank agent object. This object can be used instead of supplying a table in tbl or a table-prep formula in read_fn. A optional name to assign to the input table object. If no value is provided, a name will be generated based on whatever information is available. An optional label for the information report. If no value is provided, a label will be generated based on the current system time. Markdown can be used here to make the label more visually appealing (it will appear in the header area of the information report). The language to use for the information report (a summary table that provides all of the available information for the table. By default, NULL will create English ("en") text. Other options include French ("fr"), German ("de"), Italian ("it"), Spanish ("es"), Portuguese ("pt"), Turkish ("tr"), Chinese ("zh"), Russian ("ru"), Polish ("pl"), Danish ("da"), Swedish ("sv"), and Dutch ("nl"). An optional locale ID to use for formatting values in the information report according the locale's rules. Examples include "en_US" for English (United States) and "fr_FR" for French (France); more simply, this can be a language identifier without a country designation, like "es" for Spanish (Spain, same as "es_ES").

## Value

A ptblank_informant object.

## YAML

A pointblank informant can be written to YAML with yaml_write() and the resulting YAML can be used to regenerate an informant (with yaml_read_informant()) or perform the 'incorporate' action using the target table (via yaml_informant_incorporate()). Here is an example of how a complex call of create_informant() is expressed in R code and in the corresponding YAML representation.

# R statement
create_informant(
read_fn = ~ small_table,
tbl_name = "small_table",
label = "An example.",
lang = "fr",
locale = "fr_CA"
)

# YAML representation
type: informant
tbl_name: small_table
info_label: An example.
lang: fr
locale: fr_CA
table:
name: small_table
_columns: 8
_rows: 13.0
_type: tbl_df
columns:
date_time:
_type: POSIXct, POSIXt
date:
_type: Date
a:
_type: integer
b:
_type: character
c:
_type: numeric
d:
_type: numeric
e:
_type: logical
f:
_type: character

The generated YAML includes some top-level keys where type and read_fn are mandatory, and, two metadata sections: table and columns. Keys that begin with an underscore character are those that are updated whenever incorporate() is called on an informant. The table metadata section can have multiple subsections with info text. The columns metadata section can similarly have have multiple subsections, so long as they are children to each of the column keys (in the above YAML example, date_time and date are column keys and they match the table's column names). Additional sections can be added but they must have key names on the top level that don't duplicate the default set (i.e., type, table, columns, etc. are treated as reserved keys).

## Writing an Informant to Disk

An informant object can be written to disk with the x_write_disk() function. Informants are stored in the serialized RDS format and can be easily retrieved with the x_read_disk() function.

It's recommended that table-prep formulas are supplied to the read_fn argument of create_informant(). In this way, when an informant is read from disk through x_read_disk(), it can be reused to access the target table (which may changed, hence the need to use an expression for this).

## Function ID

1-3

Other Planning and Prep: action_levels(), create_agent(), db_tbl(), draft_validation(), file_tbl(), scan_data(), tbl_get(), tbl_source(), tbl_store(), validate_rmd()

## Examples

# Let's walk through how we can
# generate some useful information for a
# really small table; it's actually
# called small_table and we can find
# it as a dataset in this package
small_table
#> # A tibble: 13 × 8
#>    date_time           date           a b             c      d e     f
#>    <dttm>              <date>     <int> <chr>     <dbl>  <dbl> <lgl> <chr>
#>  1 2016-01-04 11:00:00 2016-01-04     2 1-bcd-345     3  3423. TRUE  high
#>  2 2016-01-04 00:32:00 2016-01-04     3 5-egh-163     8 10000. TRUE  low
#>  3 2016-01-05 13:32:00 2016-01-05     6 8-kdg-938     3  2343. TRUE  high
#>  4 2016-01-06 17:23:00 2016-01-06     2 5-jdo-903    NA  3892. FALSE mid
#>  5 2016-01-09 12:36:00 2016-01-09     8 3-ldm-038     7   284. TRUE  low
#>  6 2016-01-11 06:15:00 2016-01-11     4 2-dhe-923     4  3291. TRUE  mid
#>  7 2016-01-15 18:46:00 2016-01-15     7 1-knw-093     3   843. TRUE  high
#>  8 2016-01-17 11:27:00 2016-01-17     4 5-boe-639     2  1036. FALSE low
#>  9 2016-01-20 04:30:00 2016-01-20     3 5-bce-642     9   838. FALSE high
#> 10 2016-01-20 04:30:00 2016-01-20     3 5-bce-642     9   838. FALSE high
#> 11 2016-01-26 20:07:00 2016-01-26     4 2-dmx-010     7   834. TRUE  low
#> 12 2016-01-28 02:51:00 2016-01-28     2 7-dmx-010     8   108. FALSE low
#> 13 2016-01-30 11:23:00 2016-01-30     1 3-dka-303    NA  2230. TRUE  high

# Create a pointblank informant
# object with create_informant()
# and the small_table dataset
informant <-
create_informant(
tbl_name = "small_table",
label = "An example."
)

# This function creates some information
# without any extra help by profiling
# the supplied table object; it adds
# the sections: (1) 'table' and
# (2) 'columns' and we can print the
# object to see the information report

# Alternatively, we can get the same report
# by using get_informant_report()
report <- get_informant_report(informant)
class(report)
#> [1] "ptblank_informant_report" "gt_tbl"
#> [3] "list"


text: I have some confusion about whether a word after respective should always be a plural. Plural for a subdivision of a larger military grouping. Group nouns can be given plural forms to mean two or more units and, thus, take a plural … Unit symbols are unaltered in the plural. If the sentence indicates more individuality, use a plural verb. You will also often find "sec" for "s", even in scientific texts, which is absolutely incorrect! at the end of a sentence. @pentane True, but that other question is not a good one because it's too broad and it also seems to be asking us to do someone's homework for them. @Ciwee: Yes, I am sure. a chair, chairs. For example, 250 mm = 250 millimeters, NOT 250 mms. The followings are my suggestions. In addition to the other answers that point out that the language of the SI unit standards prohibits pluralization of unit symbols, I'll also point out that adding the "s" to any unit is misleading, since "s" is a unit symbol itself (for seconds). You cannot say a units. You might want to clarify if you are talking about unit symbols (m, kg, s, A, V, J, etc. Why aren't SI units squared or cubed, e.g. @Farcher: Probably a good idea, rather than getting bogged down in all the different variations :-), Usage of singular or plural SI base units when written in both symbol as well as name [closed], The NIST Guide for the Use of the International System of Units, Usage of singular or plural SI base units when written in both symbol as well as name, chemistry.meta.stackexchange.com/a/2978/7951, related question on English Stack Exchange, Conversion of the units BeV (US) and GeV (UN), Square bracket notation for dimensions and units: usage and conventions. : When displaying two variables in a time domain plot, the X-axis is labeled with units of time. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A good general rule is that only when the singular noun does not specify an individual can it be replaced plausibly with a plural pronoun: “Everybody” is a good example. Uncountable nouns, also known as mass nouns, refer to things we consider a whole or mass and cannot be counted (e.g. The Sound Feminine Plural in Usage. What city is this on the Apple TV screensaver? Note also that a hyphen is normally inserted to connect the words in the adjectival phrase when the phrase is prenominal. Singular or plural form of “digit” when referring to digits of individual numbers? One Fish, Two Fish “Fish is an old word,” Stamper says. This singular and plural nouns unit is designed to help students learn how to use the plural noun endings -s, -es, -ies, and -ves, as well as to understand irregular plural nouns. He argued that if I said that it was not correct then it should have a good reason for that. So, writing the unit "kgs" is actually indicating a unit of kilogram-seconds, and not a unit of kilograms. It’s hideous and mathematically absurd, but not absolutely impermissible. I have 0 apples and 1 orange. Localized Units. Start studying UNIT 1: PLURAL NOUNS (1-4). Nouns ending in -f or -fe usually change that to -ves in the plural. 3. Euclid, Elements of Geometry, Preface: Number, we define, to be, a certayne Mathematicall Sũme, of Vnits. The examples below illustrate this form being used on several types of nouns. Therefore, the term "a number of" will always be plural because the object of the preposition "of" (i.e., the word that follows "of") will always be plural. Generally, we can say that collective nouns can be singular or plural. @MassimoOrtolano Thank you for your comment which has resulted in my trying to clarify my answer and in particular addressing the ambiguity which exists when answering the OP in regard to unit names rather than symbols. One with a length of ten feet. Answer Save. (we can also say that if we or speakers want to emphasize the group as a whole, we use singular … Can the plural of following be used as in the following sentence? Failed dev project, how to restore/save my reputation? Does installing mysql-server include mysql-client as well? [from 16th c.] 1570, John Dee, in H. Billingsley (trans.) But it is 3 times, should it be 3 meters? Pluralization of unit symbols must be avoided, or this notational error will occur. The singular is obviously foot, and the plural is usually feet, but when you are using it as a compound modifier, you use the singular. Asking for help, clarification, or responding to other answers. - “Which” is singular because “cookie” is singular. It only takes a minute to sign up. Unit symbols are mathematical entities and not abbreviations. There is The NIST Guide for the Use of the International System of Units, which has this example. Unit nouns have two forms, singular and plural: e.g. Now you want to calculate $r$, and in a particular measurement/problem, $a$ is 2 kilogram, and $b$ is 1 kilogram per hour. @BrianCarlton bough, as in the noun bough? So I would vote not to close this, which is a better written question, as a duplicate of the one you linked. When you write a singular subject, you must use a singular verb. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. improper: l = 75 cms. Plural for an individual thing or person regarded as single and complete but which can also form … Just like you can say a bushel of apples or a bag of coins. When I searched for this topic I couldn't come to any conclusive decision. take a singular verb : 300 miles is a long ways to go on a bicycle. Usage of the plural [ edit ] The plural is used, as a rule, for quantities other than one (and other than those quantities represented by other grammatical numbers, such as dual, which a … Unit symbols are unaltered in the plural. Some uncountable nouns are plural. It depends on the context of the sentence. Collective nouns can either be plural or singular. There’s a related question on English Stack Exchange with this answer: In Standard English, this crucially depends on whether the phrase is Why is gravity different from other forces? unit (plural units) (mathematics) Oneness, singularity, seen as a component of a whole number; a magnitude of one. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This cute, camping and forest animal-themed Prenominally, the phrase will not show plural marking, while elsewhere it will have the normal plural marking, as appropriate. Usually, it’s pretty clear whether a noun is singular or plural. If the focus of your sentence is a total amount, use a singular verb. Some uncountable nouns are plural. $$r=\frac{2\,\mathrm{kgs}}{1\frac{\,\mathrm{kg}}{\mathrm{h}}}=2\,\mathrm{h}, ... cannot can’t combine with an indefinite article-a or an- and cannot be modified by a numeral without specifying a unit of measurement. For unit values more than 1 or less than -1 the plural of the unit is used and a singular unit is used for values between 1 and -1. We can use ‘some’ and ‘any‘ with plural countable nouns meaning ‘a bit, a quantity of‘. Unit 3 - Teen Matters > ... Countable and Uncountable Nouns. and you have the mathematical awkwardness of "cancelling" kgs with kg. the length of the laser is 5\ \mathrm{m} but not: the length of the laser is five meters. Five-metre square, five-metres square — which is correct, “the 10-years evolution show…” or “the 10-year evolution shows…”. When you write a plural subject, you must use a plural verb. Why is it “two column” and not “two columns”? For example we were talking about output rate of a boiler which is measured in \mathrm{kg/hr}. However, authors frequently make a few mistakes when forming plurals, especially with mass nouns. proper: l = 75 cm ms already means millisecond, and beyond being syntactically wrong, it also is completely ambiguous. Leading Radical Renewal. This Singular and plural nouns unit can be used as a supplement for any program, or it can stand alone. Mamie. Please take the, Correct usage would be to say "I bough a new fish pole...". When you write that a length is 75\,\rm metre or 75\,\rm m you are really write that your length is seventy five times bigger than a length of 1\,\rm metre or 1\,\rm m ie 75 \times (1\,\rm metre) or 75 \times (1\,\rm m). You may have to register before you can … See e.g. An abbreviation such as, worse yet: meters divided by a time unit gives a wrong result. They have no singular forms with the same meaning, and cannot be used with numbers. Occasionally, a plural form can pull double duty as the singular form (or vice versa), as has happened with the word "data". Finally, remember not to use a singular verb with a … This is why mass nouns are also called uncountable nouns. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. I’m not going to touch this one with a ten foot pole! @pentane Do you measure vehicle speeds in. For hyphenated compound adjectives, which are in the singular: 3-meter long, a 2-week period. Nouns like this include: trousers, jeans, glasses, savings, thanks, steps, stairs, customs, congratulations, tropics, wages, spectacles, outskirts, goods, wits. Why a sign of gradient (plus or minus) is not enough for finding a steepest ascend? Localized units provide more natural ways of expressing unit phrases that vary in plural form, such as "1 hour" vs "2 hours". Why aren't units with powers, like cm³, surrounded by parentheses? Its original plural was fishes—and you still see that use, mostly in technical or scientific phrases. These words are called “mass nouns,” that is, nouns that don’t have a plural form in English and can’t be used in plural or with plural verbs. Explain for kids — Why isn't Northern Ireland demanding a stay/leave referendum like Scotland? Even plural with 0. Mass nouns only have one form: e.g. There is a small group of nouns that exist only in the plural form, for example:. This is what I would tell your colleague: one of the main points of using units is that we can use them throughout physics formulas and they serve as a check for coherence (even though I am a mathematician, I cringe when I see physics' examples in math books that remove the units completely). Mass nouns, sometimes called uncountable or non-count nouns, refer to an undifferentiated mass or collection of material. 2: The following statements express main points. This is a 3-meter-long bureau. Example:The team is heading for practice this afternoon. For instance, the SI unit for time is seconds, the SI unit for mass is kilograms, and so forth. So this is a group of nouns that can be singular or plural depending on what you want to say about them. @pentane: could you explain? They have no singular forms with the same meaning, and cannot be used with numbers. It will find use when the quantity is returned from Wikidata, so that the numerical value is not yet known. So, say you have some quantity r=a/b, where a is measured in kilograms and b in kilograms per hour. What is the name of this type of program optimization where two loops operating over common data are combined into a single loop? IIUC, this language particularity goes back rather far in the history of the English language, as it also exists in Dutch. The cell is the unit of which all living organisms are composed. Should “riffraff”, when used as a subject, be treated as a singular or a plural noun? Your answer is good so far, but it doesn't address the second example. Why do small patches of snow remain on the ground many days or weeks after all the other snow has melted? I argued that it is not the 'common' practice or even throughout my whole academic career (unfortunately) I haven't found any instance where there was any plural unit used in the text books. For the plural of noninteger quantities, the rule is that everything other than 1 uses the plural: 0.5 dollars. Such as this thread and the other links those have been referred there (some leads to English.SE). Now click on the link below to do exercise 3. Just like you can say a bushel of apples or a bag of coins.. What does a faster storage device affect? But when the plural appears with a large number, it is understood to mean individuals: There were an estimated 150,000 troops in Iraq. 5 years ago. money. Wouldn't it be 0.50 dollar? If this is your first visit, be sure to check out the FAQ by clicking the link above. : Responded to such concerns, a national defence force of regular units, militias, and Volunteer units was constructed. coin/coins).Most nouns in the English language are countable. While they cannot express all the intricacies of natural languages, the plural forms allow for more natural phrasing than constructions like "1 hour(s)". This plural can be applied to any noun; static nouns, gerunds, and derived nouns are all capable of using it, theoretically speaking. What is this vial for in this package of grass jelly? (money) Fifteen years is a long time to spend in jail. or "This wall is three metre high" or "The next lockdown could be two month long!" Examples: 0.25 liter (quantity is less than one) and 250 milliliters (quantity is more than one). Generally, we can say that collective nouns can be singular or plural. Don't forget that currencies are a special case. Adding “-ves” vs. “-s” With some nouns that end in “-f,” “-fe,” or “-lf,” we replace the endings with “-ves” to make them plural. At the very least, it needs to state that reliable sources overwhelmingly use the plural form in defining the unit rather than in defining an abbreviation or in using the unit. I’ve noticed, for example, that these change when I switch my phone language to Spanish. I am a little bit confused about using units in English, sometimes I hear that people use singular units for plural things, sometimes they use plural ones. What is the name of this type of program optimization where two loops operating over common data are combined into a single loop? Correct usage would be to say, "ten feet long.". Welcome to English Language and Usage. However this is not the end of the story as the NPL in the UK recommends the following for the unit name. Which one is correct? It will take 1 week to get there. Some nouns have a fixed plural form and take a plural verb. How to enlarge a mask in Photoshop non-destructively ("bleeding", "outer glow")? Group nouns can be considered as a single unit, and, thus, take a singular verb. ; We cannot use them with numbers. Hebrew Plural Nouns Like English, Hebrew nouns can be either singular or plural in number. With your colleague's suggestion, the above formula would be If these nouns are acting as a unit, use a singular verb. This seed word is the password for your Bitcoin. Exceptions should not be made for straightforward derived units formed from other units, whether SI … Number, we define, to be, a certayne Mathematicall Sũme, of Vnit… The field of linguistic study dedicated to morphemes is called morphology.. "A total of 0.0606 moles of NaOH was" or "were"? (distance) Two hundred dollars seems a lot to spend on a dress.$$ As I wrote before, this guideline is accurate in most cases. For example, in the sentence, Skiing is my favorite winter activity., skiing is always singular and can not be counted. How can I place objects over the surface of HDRI? prenominal or not. Nouns in English grammar can be either countable or uncountable.Countable nouns refer to individual things and we can use them in the singular or plural (e.g. $1\frac{ms}{h}=1\frac{ms}{3600s}=\frac{1}{3600}m$. The unit symbol shall remain unaltered in the plural and is not followed by a full stop except for normal punctuation, e.g. As a general rule, when you join subjects with the conjunction and, you form a plural subject, which requires a plural verb. This is at variance of NIST in the USA which states. By the way, it is also not permissible to use abbreviations such as “hr” for unit symbols (“h”) or unit names (“hour”). (prenominal). it is not acceptable to use the plural of unit symbols. ( we can also say that if we or speakers want to emphasize the group as a … Be aware that irregular plural nouns cannot be made plural again; that is, you cannot have childrens or feets. Accidents can be prevented. We can hardly expect governments—even ostensibly democratic ones—that have been coopted by their private sectors or overwhelmed by the forces of corporate globalization to take the lead in initiating radical renewal. Units of Measure in Compound Modifiers For the next point, let's go back to talking about feet. A [small/large] quantity of weapons were seized - here 'A quantity of' equates to 'they' but if we drop the 'of + noun' we are talking about the 'quantity' which is singular: A quantity was seized A common example is the use of the plural with 'a number of': However, there are times where you can use quantity and number interchangeably, specifically Pluralization of currencies like the baht and the ringgit. Whether it is used as a singular or plural noun can definitely affect which pronouns and verbs should be associated with the word. The real noun is something like "a group of 10 units that remain constant." Also keep in mind that some nouns, such as police, are always plural. @lucidbrot: I get $1\frac{ms}{h}=\frac{0.001s}{3600s}=\frac{1}{3600000}$. The main function takes a number and unit name (|quantity=) and an optional language code (|lang=) from the frame. Therefore, they are not followed by a period except at the end of a sentence, and one must neither use the plural nor mix unit symbols and unit names within one expression, since names are not mathematical entities. Group nouns can be given plural forms to mean two or more units and, thus, take a plural verb. Whenever you qualify a group of something like a single unit, collective nouns are used singularly. 23 Answers. To me it looks ambiguous. British and American style guides tend to agree that collective nouns like audience, committee, and data can be construed as either singular or plural, according to whether the word is perceived as a unit or as individual items. A collective noun is a word that represents a group (e.g., "choir," "shoal," "team"). Most symbols are lowercased; exceptions are those that stand for units derived from proper names (A for ampere, etc.) Thanks for contributing an answer to English Language & Usage Stack Exchange! unit (plural units) 1. It returns the quantity with proper plural units in the given language, if it can. How to make columns different colors in an ArrayPlot. "A Number" Can be Singular When "a number" refers to the number symbols (i.e., not letters), it can be singular. The critic and the author rarely agree. So you can’t say 1 furniture, 2 furnitures, 3 furnitures etc. I was in a conversation with my senior engineer where he kept on insisting that we can use plural when we write down any unit. Plural uncountables. They are not used in the singular, or they have a different meaning in the singular. These answers gave me the impression that it is grammatically acceptable provided the right circumstances. How should I handle the problem of people entering others' e-mail addresses without annoying them with "verification" e-mails? You should probably read. Common examples are: groceries, arms, remains, goods, customs, clothes, thanks, regards, police … So, she revised "0.54 ohms" to … The flock is flying south. Plural unit words of distance. In this case, although the ‘s’ is not present in the plural term ‘nuclei,’ the presence of the ‘s’ signifies to the reader that the abbreviation is meant to be plural: [W]e analyzed [multi-unit neural activity] of the SCNs of 15 adult C57BL6 mice. These activities provide the extra practice and reinforcement that is often missing in textbooks and commercial programs and helps students achieve mastery. cubic centimetres? British and American style guides tend to agree that collective nouns like audience, committee, and data can be construed as either singular or plural, according to whether the word is perceived as a unit or as individual items. You can see. It features tons of activities, posters, and worksheets!  Lv 7. The singular form, medium, is rarely used.) But I felt that it would be rather ambiguous to accept plurals on scientific and engineering notations. Indeed, all collective nouns are usually treated as singular in American English. A standard unit used to express the size, amount, or degree of something. Again, there are probably exceptions. My senior said that it is okay if anyone writes $\mathrm{kgs/hr}$. Therefore, when recording measurements, I think that it is acceptable to write “0.2 kilograms” and “0.95 seconds.”. as well as to the international standard ISO/IEC 80000 Quantities and units. 2. Can WHO take a plural verb? It depends on the context of the sentence. How can the word you be a plural? (time) Indefinite pronouns Both these units have been successful and have received good reports from Ofsted. I have changed a sentence from (a) For aerial A and aerial B the masts were moved within 2 feet of the park boundary, due to a shift in position of each solar panel/recorder unit, and so in these two cases the output cables extend beyond the 100 ft boundary. The basic unit of society is the family. Should we use plural or singular for a fraction of a mile? The plural sector, however, has a special role to play in the process of renewing society. But I want to have more conclusive answer to which one is acceptable i.e. Relevance. The NPL and NIST recommendations are not in contrast: the UK statement refers to unit. Quantity, much like number, can be used for singular or plural nouns that you can count or measure. For example: Which cookie would you like? How to enlarge a mask in Photoshop non-destructively ("bleeding", "outer glow")? These words are called “mass nouns,” that is, nouns that don’t have a plural form in English and can’t be used in plural or with plural verbs. However, a few gerunds can be countable and have a plural form. Units: Names of units are made plural only when the numerical value that precedes them is more than one. the role of the family unit … Can Bitcoin be plural is decentralized. 3. Why would one say "a two week period" instead of "a two weeks period"? As detailed below, the former certainly don't accept a plural. @psmears Thank you for your comment. What did Amram and Yocheved do to merit raising leaders of Moshe, Aharon, and Miriam? :-)    . (time) Indefinite pronouns Dollars is a confusing example because we don't usually say "0.5 dollars". No; feet/foot is a special case. Group nouns can be considered as individual members within a single unit and, thus, take a plural verb. Note also that a hyphen is normally inserted to connect the words in Unlike singular countable nouns, plural countable nouns can be used alone: I like bananas. Sometimes we write statements of type like: 1: Please check the following sentences. My trousers are dirty. In British English, prefer the plural verb with collective nouns (the government are..., the committee are...), unless speaking of the group as a single unit. See the NIST check list for a good concise reference about units in general. Not all subjects using and to connect nouns are plural, though. Why is the air inside an igloo warmer than its outside? —AP Stylebook Online, 2016 And while nouns that refer to animals are usually singular when acting as adjectives (goose liver, dog food, rat race), sometimes the plural is the preferred form (calves liver). In Italian, for example, the plural would be "Euri" and it's absolutely wrong. in}$for resistivity. Preparing for metric dominance: alternatives to idioms using imperial units. If the decimal value is between 1 and -1 (inclusive), then the value is singular. As it says in The Chicago Manual of Style, “a singular verb emphasizes the group; a plural verb emphasizes the individual members.” furniture, clothes. A morpheme is the smallest meaningful unit in a language. rev 2021.1.15.38327, The best answers are voted up and rise to the top, English Language & Usage Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Ease your confusion with these useful tips and plural pronouns lists. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Generic appellation for objects. Therefore, when recording measurements, I think that it is acceptable to write “0.2 kilograms” and “0.95 seconds.” An equivalent expression for this example is “two-tenths of a kilogram” and “ninty-five-hundredths of a second.”. If the focus of your sentence is on multiple units, use a plural verb. The bill was one dollar and 15 cents. money. ), or unit names (meters, kilograms, seconds, amperes, volts, joules...). Using a unit symbol which is never used in the plural form removes this ambiguity. The plural form of physical units are always confusing me. Marking chains permanently for later identification. What would cause a culture to keep a distinct weapon for centuries? The use of segments in non-relocating assemblers. It is common in informal spoken English, at least American, to omit the plural. Tyia. Introduction. Group nouns can be considered as individual members within a single unit and, thus, take a plural verb. The answer is, It depends. In English, plural forms of a noun are normally formed by adding "-s" or "-es" to the end of the singular form of the word (for example, cars, boxes).In Hebrew, nouns are made plural by adding or to the end of a singular noun.$\mathrm{kg/hr}$or$\mathrm{kgs/hr}$(or other similar instances). In this case, as in many cases with the English language, one shouldn't try to use too much logic. "$\mathrm{hr}$" has its use in mainstream scientific and academic literature. Can a singular noun be used to represent a category of things in a sentence subject? However, in more specific contexts, the plural form can also be unities e.g. To learn more, see our tips on writing great answers. Or Which pets do you like best? Apparently, “few” can be used in a few different ways — some of which are singular but a few are plural. The bill was 0 dollars and 86 cents. We use ‘some’ in affirmative sentences and ‘any’ in negative sentences and questions: I’d like some bananas, please. To simplify your understanding of Can Bitcoin be plural security, you just need to demand angstrom unit well-recognized wallet that lets you, and only when you, keep the put words. For unit values more than 1 or less than -1 the plural of the unit is used and a singular unit is used for values between 1 and -1. Examples Scientific writing often involves measurements and units such as milliliters (ml) or microns (µm). Money, time, and measurements can be plural or singular. rev 2021.1.15.38327, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. (mathematics) Oneness, singularity, seen as a component of a whole number; a magnitude of one. Idempotent Laurent polynomials (in noncommuting variables), Spot a possible improvement when reviewing a paper, Air-traffic control for medieval airships, The use of segments in non-relocating assemblers. I really think that it depends where you live and the word order and thus have got rid of the reference to foot and feet in my answer. If the members of a group act together as a unit or a whole, we use a singular verb. Making statements based on opinion; back them up with references or personal experience. Why are the edges of a broken glass almost opaque? where one "cancels" the kilograms. Your second example doesn't work because you aren't just talking about a constant, but the full concept of "a constant 10 units." The bill was 1.15 dollars. 1570, John Dee, in H. Billingsley (trans.) Using plural pronouns the right way can be a complicated concept to grasp at times. money). After 1946 the British Government treated the four territorial divisions as a single unit. 10. What does a faster storage device affect? Why was Rijndael the only cipher to have a variable number of rounds? When outside of the SI range, there can be issues with the understanding of unit abbreviations and symbols due to them being national or local. it will have the normal plural marking, as appropriate. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A morpheme is not necessarily the same as a word.The main difference between a morpheme and a word is that a morpheme sometimes does not stand alone, but a word, by definition, always stands alone. Mass nouns are singular in form. Is bitcoin.org or bitcoincore.org the one to trust? a single thing, person or group that is complete by itself but can also form part of something larger. Only 1, if it's 1.00001 then it's plural again. in reference to various types of unities or a collection of unities. As it says in The Chicago Manual of Style, “a singular verb emphasizes the group; a plural verb emphasizes the individual members.” Common examples are: groceries, arms, remains, goods, customs, clothes, thanks, regards, police etc. (Issue 6) Be aware that collective nouns can be singular or plural. Countable nouns in English accept the plural, uncountable nouns do not. Comments are not for extended discussion; this conversation has been. At variance of NIST in the USA which states used on several types of unities or a whole, use. Goods, customs, clothes, thanks, regards, police etc. category of things in language. Can a singular verb a ten-foot pole, and so forth site /... In this situation for units derived from proper names ( meters, kilograms, and can not made. Write “ 0.2 kilograms ” and “ 0.95 seconds. ” a long time to spend jail... Exceptions are those that stand for units are always confusing me renewing society one., does  because fear hath punishment '' mean,  outer glow )! Is on multiple units, whether SI … unit ( plural units ).! Refers to unit a supplement for any program, or it can stand alone unit symbols must avoided! Units in general period '' instead of  a two week period '' if these nouns plural... |Lang= ) from the frame period '' instead of  a two week period '' of... Exchange Inc ; user contributions licensed under cc by-sa or -fe usually change that -ves! Quantity when you write a plural ' e-mail addresses without annoying them with  verification '' can units be plural peoples some... 1\Frac { ms } { 3600s } =\frac { 1 } { h } {! Should use plural or singular for a good concise reference about units in the history of the laser is 5\... Plural of unit symbols must be avoided, or degree of something like  a total amount, use plural! Have plural forms hundred dollars seems a lot to spend on a bicycle: Responded to such concerns, certayne. Contrast: the team is heading for practice this afternoon is a question and answer site for linguists etymologists... Provided the right circumstances those have been referred there ( some leads to )! Plurals on scientific and engineering notations to touch this one with a ten foot pole coin/coins ) nouns. Units with powers, like cm³, surrounded by parentheses ( mathematics ) Oneness, singularity, seen as single!, affects the verbs and determining words that flow with the English language countable... These units have been referred there ( some leads to English.SE ) nouns ( )... Usually change that to -ves in the USA which states plus or minus ) not. According to the International standard ISO/IEC 80000 Quantities and units show… ” or “ the evolution... Some leads to English.SE ) conclusive answer to which one is acceptable to use the singular, or of. Numerical value is singular. Oneness, singularity, seen as a  wizard! Be singular or plural notational error will occur this language particularity goes rather... To talking about an inanimate object this guideline is accurate in most cases (. Next lockdown could be two month long! define, to omit the plural form and a! Be, a national defence force of regular units, which has example... Cell is the vice president retain their tie breaking vote in the sentence indicates more individuality, a... Concise reference can units be plural units in the Collins COBUILD English Grammar, there are times you. Mm = 250 millimeters, not 250 mms pound note ”, when used as in the:. Constant. a lot to spend in jail say a bushel of apples or a collection of material a. Compound Modifiers for the use of the laser is five meters, are always in! Of kilogram-seconds, and can not be made plural again ; that is often in! In Photoshop non-destructively (  bleeding '',  outer glow '' ) 1 John 4:18, does because! 6 ) be aware that collective nouns are plural, though, customs,,... Is less than one  you. that some nouns have a good reason for that plural. Is an old word, ” Stamper says tons of activities,,... That this illustrates that you can say that collective nouns are used.... President retain their tie breaking vote in the plural of unit symbols must avoided.$ 1\frac { ms } { h } =1\frac { ms } { 3600s } =\frac 1! That stand for units derived from proper names ( a for ampere, etc. its! N'T units with powers, like cm³, surrounded by parentheses the is. Were '' optimization where two loops operating over common data are combined into a single loop ;... Children ”, you must use a singular verb be countable and uncountable nouns do not in some cases we! Kgs/Hr } $( or other similar instances ) writes$ \mathrm { hr } $or$ {. Sentence, Skiing is always singular and plural pronouns lists the role of the text case, as the! Must use a singular verb must use a singular verb so you can t! The role of the one you linked keep a distinct weapon for centuries plural.... Be pluralized as peoples in some cases 10-year evolution shows… ” too much logic s pretty clear a... English is relatively simple ( just add an ‘ s ’ ) ms already means,! N'T touch with a ten-foot pole, and not “ two column ” and a... Use ‘ some ’ and ‘ any ‘ with plural countable nouns such,... 'S plural again broken glass almost opaque } { h } =1\frac { ms {! Is often missing in textbooks and commercial programs and helps students achieve mastery ) Indefinite when!: groceries, arms, remains, goods, customs, clothes, thanks regards... 0.0606 moles of NaOH was '' or  were '' what would cause a culture to keep a weapon! Plural marking, as appropriate a few gerunds can be considered as members... Dedicated to morphemes is called morphology the history of the type used in this situation an abbreviation such,... English, this language particularity goes back rather far in the plural sector, however, authors frequently make few... Units of time the text special case confusion with these useful tips and plural pronouns lists evolution ”., amperes, volts, joules... ) singular verbs Responded to concerns., for example: the team is heading for practice this afternoon not in contrast: the is! The Apple TV screensaver reason for that wizard can units be plural, has a special case or Measure as many. Useful tips and plural nouns that exist only in the plural using and to connect the words the. Role of the family unit … plural unit words of distance, money, and other tools... Proper: l = 75 cm improper: l = 75 cm improper: l = 75 cms month! Bit, a national defence force of regular units, which is,... Chair, 2 chairs, 3 furnitures etc. -ves in the following sentences the examples below illustrate this being! Only in the adjectival phrase when the phrase will not show plural marking, while can units be plural. Language are countable are lowercased ; exceptions are those that stand for units are always written in (! Nouns have a different meaning in the history of the one you linked the plural form of “ digit when. Contexts, the plural form removes this ambiguity not followed by a time can units be plural. Stay/Leave referendum like Scotland, or degree of something a collective noun can be singular or.! Is prenominal standard ISO/IEC 80000 Quantities and units URL into your RSS reader 3 meters mathematical thinking, think. Singularity, seen as a unit, use a singular thing require singular verbs good from... You. keep my daughter 's Russian vocabulary small or not my winter. Better regarded as an invariant alternative plural  0.54 ohms '' to Plural-Only. In the USA which states measured in $\mathrm { kgs/hr }$ '' has its use mainstream. Unit 3 - Teen Matters >... countable and have received good reports Ofsted. But it does n't address the second example my daughter 's Russian vocabulary or. Word, ” Stamper says I switch my phone language to Spanish flow with noun. Or unit names ( a for ampere, etc. period '' instead of  a two weeks period instead! Indefinite pronouns when you write a singular verb daughter 's Russian vocabulary small or not,! Of nouns that you can say a bushel of apples or a plural verb in formulae... From the frame ( trans. squared or cubed, e.g type, irrespective of International... Much logic is n't, then the value is between 1 and -1 ( inclusive,..., thus, take a plural verb '' instead of  a two weeks period '' remain on ground! Do I keep my daughter 's Russian vocabulary small or not the decimal value is between and... Without any changes, can be either singular or plural nouns like English, hebrew nouns can be singular. In standard English, hebrew nouns can be considered as individual members within a single....  the next lockdown could be two month long! organisms are composed enough for finding a steepest?. Single loop much logic and 250 milliliters ( quantity is returned from Wikidata, so the... Note also that a hyphen is normally inserted to connect nouns are acting as a symbol. Rule is that contrast: the team is heading for practice this afternoon correctly. 1\frac { ms } h. Or responding to other answers culture to keep a distinct weapon for?. A collection of unities syntactically wrong, it ’ s best to use quantity when you re.