Tuesday, April 23, 2024, 4:48 AM
Site: Saint Martin's University Moodle
Course: Saint Martin's University Moodle (SMU)
Glossary: Math Notation Help
01 GETTING STARTED
escaping the TeX filter - With two triple $'s embracing an expression you can make the filter to escape and the code itself is shown (with two embracing double $'s).
- Ex.: $$$a^2$$$ produces $$a^2$$, i.e. prevents the filter to render it as a formula gif.
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mathematics expression - A valid expression inside the $'s is rendered as mathematics in an inserted gif image.
- Ex.: $$x=y^2$$ creates
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triggering the TeX filter - Two double $'s embracing a valid math expression trigger the filter to generate and insert the formula gif.
- Ex.: $$a^2$$ produces
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02 ARITHMETIC EXPRESSIONS, SUB-/SUPERSCRIPTS, ROOTS
arithmetic operations - Type arithmetic operations and "=" as usual.
- Exp.: $$f(x)=x-2b+(3a/c)$$ gives
- See also keyword "fraction" for extended capabilities.
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constants - Numbers in formulas are interpreted as constants and they are rendered in non-italic roman font face, which is a widely used convention.
- Following this convention, variables are shown in italic.
- Exp.: $$f(x)=3a+x$$ gives
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fraction - Syntax: \frac{numerator}{denominator}
- Use font sizing commands for specific sizing if you don't want the predefined one to be taken.
- Ex. (with predefined sizing): $$f(x,y)=\frac{2a}{x+y}$$ gives
- Ex. (with specific sizing): $$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$$ gives
- You may nest fractions as much as you want.
- Ex. (nested fractions): $$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$$ gives
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multiplication (with cdot) $$a\cdot~b$$ gives |
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root - Syntax: \sqrt[n]{arg} or simply \sqrt{arg} for \sqrt[2]{arg}
- Ex.: $$\sqrt[3]{8}$$ gives
- Nesting of roots (and combining with fractions, ...etc.) are possible.
- Ex.: $$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$$ gives
- Ex.: $$\sqrt[3]{-q+\sqrt{q^2+p^3}}$$ gives
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square root - $$\sqrt{a}$$ or $$\sqrt~a$$ gives
- Use braces for terms with more than one character: $$\sqrt{x+y}$$ gives
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subscript - The command character "_" triggers subscription of the following expression(s).
- For more than one subscripted character put them in braces {...}.
- Use font sizing commands for appropriate sizing.
- Ex.:$$x_1$$ gives
- Ex. (with specific sizing): $$x_{\small1}=a_{\small{m+2n}}$$ gives
- Combine subscripting with superscripting (command character "^").
Syntax: Expr_{subExpr}^{supExpr}. - Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives
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superscript - The command character "^" triggers superscription of the following expression(s).
- For more than one superscripted character put them in braces {...}.
- Use font sizing commands for appropriate sizing.
- Ex.: $$x^2$$ gives
- Ex. (with specific sizing): $$x^{\small2}=a^{\small{m+2n}}$$ gives
- Combine superscripting with subscripting (command character "_").
Syntax: Expr_{subExpr}^{supExpr}. - Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}$$ gives
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variables - Variables in formulas are rendered in italic roman font face, which is a widely used convention.
- Following this convention, constants are shown as non-italic.
- Exp.: $$f(x)=3a+x$$ gives
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03 FONT STYLES
\LARGE (all capital letters) - Everthing following the \LARGE command will be output in the largest predefined font size until the system encounters another font size command.
- Note: This command is case sensitive, since large, Large and LARGE are different sizes!
- Ex.: $$\LARGE~3x$$ gives
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\Large (L capital letter) - Everthing following the \Large command will be output in the second largest font size until the system encounters another font size command.
- Note: This command is case sensitive, since large, Large and LARGE are different sizes!
- Ex.: $$\Large~3x$$ gives
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\large (all lower case letters) - Everthing following the \large command will be output in the large font size until the system encounters another font size command.
- Note: This command is case sensitive, since large, Large and LARGE are different sizes!
- Ex.: $$\large~3x$$ gives
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\normalsize - Everthing following the \normalsize command will be output in the smallest predefined font size until the system encounters another font size command.
- \normalsize is the default font size, i.e. the size automatically chosen if there is no font size command
- Ex.: $$\normalsize~3x$$ gives
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\small - \small
- Ex.: $$\small~3x$$ gives
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\tiny - Everthing following the \tiny command will be output in the smallest predefined font size until the system encounters another font size command.
- Ex.: $$\tiny~3x$$ gives
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absolute font sizes (overview) |
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04 DELIMITERS (PARENTHESES, BRACES,...)
angle bracket - Syntax: \left<...\right>
- Ex.: $$\left<f,g\right>$$ gives
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braces - Syntax: \left{...\right}
- Ex.: $$M=\left{a, b, c\right}$$ gives
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delimiters (overview) Delimiters (parentheses, braces, brackets. ...) | Command | Example | Result | \left(... \right) | $$2\left(a+b\right)$$ | | \left[... \right] | $$\left[a^2+b^2~\right]$$ | | \left{... \right} | $$\left{x^2, x^3, x^4,... \right}$$ | | \left\langle... \right\rangle | $$\left\langle a,b~\right\rangle$$ | | \left| ... \right| | $$\det\left|\array{a&b\\c&d}\right| $$ | | \left\| ... \right\| | $$\left\|f~\right\|$$ | | \left{ ... \right. (note the dot!) | $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ (\rm switches to roman style) |
| \left.{ ... \right\} (note the dot!) | $$\left.{{\rm~term1\atop\rm~term2}\right}=y$$ | | | | |
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Note: The delimiters are automatically sizes. |
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double vertical line (norm symbol) - Syntax: \left\|...\right\|
- Exp.: $$\left\|af\right\| = \left|a\right|\left\|f\right\|$$ gives
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left only brace - Syntax: \left{...\right. (note the dot at the end!)
- Ex.: $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ gives
(\rm~something switches to roman style) |
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parentheses - Syntax: \left(...\right) or
- Ex.: $$2a\left(b+c\right)$$ gives
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right only brace - Syntax: \left.{...\right} (note the dot!)
- Ex.: $$\left.{{\rm~term1\atop\rm~term2}\right}=y$$ gives
(\rm~something switches to roman style) |
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square bracket - Synatx: \left[...\right]
- Ex.: $$\left[a,b\right]$$ gives
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vertical line (absolute value, determinant, ...etc. symbol) - Syntax: \left|...\right|
- Ex.: $$\left|b-a\right|$$ gives
- Ex.: $${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$$ gives
("\rm~something" renders "something" in roman style) |
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05 SPACES
\_ (where _ is blank) - Ordinary whitespace to be used after a dot not denoting the end of a sentence
- After commands without parameters use \~ (tilde) instead in order to avoid browser specific problems
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\, - \, inserts the smallest predefined space in a formula
- Equivalent: \hspace{2}
- Ex.: $$a\,b$$ gives
- Ex.: $$a~\hspace{2}~b$$ gives also
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\; - \; (backslash semicolon) inserts the third smallest predefined space in a formula
- Equivalent: \hspace{6}
- Ex.: $$a\;b$$ gives
- Ex.: $$a~\hspace{6}~b$$ gives also
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\: - \: inserts the second smallest predefined space in a formula
- Equivalent: \hspace{4}
- Ex.: $$a\:b$$ gives
- Ex.: $$a~\hspace{4}~b$$ gives also
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\/ (backslash slash) - \/ (backslash slash) avoids ligatures
- Ex.: $$V\/A$$ gives in contrast to $$VA$$ which gives
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\~ - In order to prevent some browser specific problems with whitespaces, it is advisable to use ~ (tilde) as the whitespace instead of the normal blank key (in places where whitespaces are mandatory, e.g. after commands).
- Ex.: $$\frac~xy$$ to produce
- Ex.: $$\sqrt~n$$ to produce
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\hspace{n} - inserts a space of n pixels
- Ex.: $$f(x)\hspace{6}=\hspace{6}0$$ gives
- can be combined with the preceding command \unitlength{m}(default: m=1px) , which defines the applied unit
- Ex.: $$\unitlength{20}a\hspace{2}b$$ gives , i.e. a space of 20x2=40px
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\qquad - inserts a double space of current character set size
- Ex.: $$a\qquad~b$$ gives
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\quad - inserts a space of current character set size
- Ex.: $$a\quad~b$$ gives
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math spaces List of predefined spaces: Math Spaces | Command | Example | Result | \, (smallest predefined) | $$a\,b$$ | | \: (second smallest predefined) | $$a\:b$$ | | \; (third smallest predefined) | $$a\;b$$ | | \/ (avoiding ligatures) | $$V\/A$$ instead of $$VA$$ | instead of | \quad (space of current character set size) | $$a\quad~b$$ | | \qquad (double space of current character set size) | $$a\qquad~b$$ | | \_ (where _ is blank!) | $$a\ b$$ (whereas $$a\b$$ is not a valid filter expression since the blank space is missing; it is recommended to use the tilde ~ instead of the simple whitespace) |
| \hspace{n} ,where n positive integer (= n Pixels) | $$a~\hspace{30}~b$$ $$a~\hspace{15}~b$$ $$a~\hspace{2}~b$$ $$a~\hspace{1}~b$$ |
| \unitlength{m}\hspace{n}, changes the default unit length (m=1px) to be applied | $$a~\hspace{2}~b\unitlength{10}~\hspace{2}~c$$ (second space is 10x2=20px) | |
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Note: Simple blank spaces and tildes (~) are ignored by the TeX filter and don't produce any space. You must use one of the defined math spaces to get a visible (extra) space. |
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06 SYMBOLS
alpha (lower case greek letter) $$\alpha$$ gives |
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beta (lower case greek letter) $$\beta$$ gives |
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cdot (multiplication) $$a\cdot~b$$ gives |
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chi (lower case greek letter) $$\chi$$ gives |
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contour integral - General syntax for symbols with a kind of lower and upper limits:
\symbolname_{lowerexpression}^{upperexpression} - In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
- Syntax for the contour integral symbol:
$$\bigoint_{0}^{\infty}$$ gives and $$\oint_{0}^{\infty}$$ gives
$$\LARGE\bigoint_{\small0}^{\small\infty}$$ gives and $$\large\oint_{\small0}^{\small\infty}$$ gives |
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coproduct - General syntax for symbols with a kind of lower and upper limits:
\symbolname_{lowerexpression}^{upperexpression} - In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
- Note: mimeTeX seems currently only to support the \bigcoprod command.
- Syntax for coproduct symbol:
$$\bigcoprod_{i=k}^{n}$$ gives $$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$$ gives |
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Delta (upper case greek letter) $$\Delta$$ gives |
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delta (lower case greek letter) $$\delta$$ gives |
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div (division) $$x\div~y$$ gives |
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epsilon (lower case greek letter) $$\epsilon$$ gives |
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eta (lower case greek letter) $$\eta$$ gives |
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gamma (lower case greek letter) $$\gamma$$ gives |
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Gamma (upper case greek letter) $$\Gamma$$ gives |
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infinity $$\infty$$ gives |
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integral - General syntax for symbols with a kind of lower and upper limits:
\symbolname_{lowerexpression}^{upperexpression} - In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
- Syntax for integral symbol:
$$\bigint_{0}^{\infty}$$ gives and $$\int_{0}^{\infty}$$ gives
$$\LARGE\bigint_{\small0}^{\small\infty}$$ gives and $$\large\int_{\small0}^{\small\infty}$$ gives |
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iota (lower case greek letter) $$\iota$$ gives |
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kappa $$\kappa$$ gives |
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lambda (lower case greek letter) $$\lambda$$ gives |
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Lambda (upper case greek letter) $$\Lambda$$ gives |
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minus plus $$\mp~a$$ gives |
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mu (lower case greek letter) $$\mu$$ gives |
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nu (lower case greek letter) $$\nu$$ gives |
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omega (lower case greek letter) $$\omega$$ gives |
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Omega (upper case greek letter) $$\Omega$$ gives |
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omikron (lower case greek letter) $$o$$ gives (note this exceptional syntax!) |
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phi (lower case greek letter) $$\phi$$ gives |
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Phi (upper case greek letter) $$\Phi$$ gives |
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pi (lower case greek letter) $$\pi$$ gives |
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Pi (upper case greek letter) $$\Pi$$ gives |
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plus minus $$a\pm~b$$ gives |
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product - General syntax for symbols with a kind of lower and upper limits:
\symbolname_{lowerexpression}^{upperexpression} - In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
- Syntax for product symbol:
$$\bigprod_{i=k}^{n}$$ gives and $$\prod_{i=k}^{n}$$ gives
$$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}$$ gives and $$\large\prod_{\small{i=k}}^{\small{n}}$$ gives |
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psi (lower case greek letter) $$\psi$$ gives |
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Psi (upper case greek letter) $$\Psi$$ gives |
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rho (lower case greek letter) $$\rho$$ gives |
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sigma (lower case greek letter) $$\sigma$$ gives |
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Sigma (upper case greek letter) $$\Sigma$$ gives |
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sum (summation) - General syntax for symbols with a kind of lower and upper limits:
\symbolname_{lowerexpression}^{upperexpression} - In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
- Syntax for summation symbol:
$$\bigsum_{i=k}^{n}$$ gives and $$\sum_{i=k}^{n}$$ gives
$$\LARGE\bigsum_{\small{i=1}}^{\small{n}}$$ gives and $$\large\sum_{\small{i=1}}^{\small{n}}$$ gives |
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tau (lower case greek letter) $$\tau$$ gives |
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theta (lower case greek letter) $$\theta$$ gives |
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Theta (upper case greek letter) $$\Theta$$ gives |
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times $$a\times~b$$ gives |
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upsilon (lower case greek letter) $$\upsilon$$ gives |
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Upsilon (upper case greek letter) $$\Upsilon$$ gives |
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varepsilon (special lower case greek letter) $$\varepsilon$$ gives |
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varphi (special lower case greek letter) $$\varphi$$ gives |
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varpi (special lower case greek letter) $$\varpi$$ gives |
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varrho (special lower case greek letter) $$\varrho$$ gives |
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varsigma (special lower greek letter) $$\varsigma$$ gives |
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vartheta (special lower case greek letter) $$\vartheta$$ gives |
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xi (lower case greek letter) $$\xi$$ gives |
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Xi (upper case greek letter) $$\Xi$$ gives |
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zeta (lower case greek letter) $$\zeta$$ gives |
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07 RELATIONS
greater than $$x>y$$ gives |
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greater than or equal $$x\ge~y$$ or $$x\geq~y$$ gives |
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less than $$<$$ gives |
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less than or equal $$x\le~y$$ or $$x\leq~y$$ gives |
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not equal $$x\neq~y$$ gives note: \neg produces the logical negation, i.e. $$\neg~A$$ gives |
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09 STRUCTURES
array - Syntax for an n-dimensional array:
\begin{array}a1&...&an\end{array} - Ex.: $$$$ gives
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matrix - An (m,n)-matrix is considered as an array of m*n elements, where the elements of a column are separated by "&" and the rows by "\\".
Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned. |
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