Number

fraction

$\frac{1}{2}$

\frac{1}{2}

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\frac comes from "fraction". The first wave brackets is for the numerator and the second is for the denominator.

fraction large

$\displaystyle \frac{1}{2}$

\displaystyle \frac{1}{2}

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If you add "\displaystyle", it will be displayed larger.

fraction large 2

$\dfrac{1}{2}$

\dfrac{1}{2}

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\dfrac means \frac in \displaystyle.

fraction one line

$\require{physics} \flatfrac{1}{2}$

\require{physics} \flatfrac{1}{2}

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\flatfrac in the physics extension allows you to write fractions on a line. You can also use the sign / to write "1/2".

fraction and parentheses

$\left( -\frac{1}{2} \right)^2$

\left( -\frac{1}{2} \right)^2

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To keep the fractions in parentheses, prefix the brackets with \left and \right.

fraction and parentheses 2

$\require{physics} \qty( -\frac{1}{2} )^2$

\require{physics} \qty( -\frac{1}{2} )^2

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\qty in the physics extension allows you to write parenthesized fractions a little simpler. \qty comes from physical quantity.

continued fraction

$\frac{a+b}{c+\frac{d}{e}}$

\frac{a+b}{c+\frac{d}{e}}

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Fractions can be nested.

continued fraction 2

$\cfrac{a+b}{c+\cfrac{d}{e}}$

\cfrac{a+b}{c+\cfrac{d}{e}}

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With \cfrac, the size of the fraction will be the same. \cfrac comes from continued fraction. Using \dfrac would produce a similar display.

infinite continued fraction

$\begin{eqnarray} 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}} = \frac{1}{2} \left( 1+\sqrt{5} \right) \end{eqnarray}$

\begin{eqnarray}
1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}
= \frac{1}{2} \left( 1+\sqrt{5} \right)
\end{eqnarray}

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The diagonal dots indicate that it goes on forever.

decimal

$0.123$

0.123

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A period is used for the decimal point.

repeating decimal

$\frac{1}{11} = 0.\dot{0}\dot{9}$

\frac{1}{11} = 0.\dot{0}\dot{9}

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To add dot on top of a number, use \dot.

infinite decimal 1

$\pi = 3.14 \ldots$

\pi = 3.14 \ldots

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Here's a sample to add three points to the bottom.

infinite decimal 2

$\sqrt{2} = 1.4142 \cdots$

\sqrt{2} = 1.4142 \cdots

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Here's a sample to add three points in the middle.

infty

$\infty$

\infty

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\infty comes from "infinity".

absolute value

$|x|$

|x|

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Absolute values can be represented by a vertical line symbol.

absolute value 2

$\vert x \vert$

\vert x \vert

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A vertical line used for absolute values can also be represented by vert, which comes from vertical line.

fraction and absolute value

$\left| \dfrac{x}{2} \right|$

\left| \dfrac{x}{2} \right|

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If you add \left and \right before the vertical lines, the vertical lines will be longer to match the size of the fraction.

fraction and absolute value 2

$\require{physics} \qty|\dfrac{x}{2}|$

\require{physics} \qty|\dfrac{x}{2}|

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\qty in the physics extension allows you to write fractions with absolute value symbols a little simpler. \qty comes from physical quantity.

fraction and absolute value 3

$\require{physics} \abs{ \dfrac{x}{2} }$

\require{physics} \abs{ \dfrac{x}{2} }

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\abs in the physics extension allows you to write fractions with absolute value symbols. \abs comes from "absolute value".

Gaussian brackets

$[x]$

[x]

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The Gauss brackets can be represented by a square bracket symbol.

Gaussian brackets 2

$\lbrack x \rbrack$

\lbrack x \rbrack

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The Gauss brackets can also be represented with \lbrack and \rblack. They come from the left bracket and the right bracket.

floor function

$\lfloor x \rfloor$

\lfloor x \rfloor

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They come from "floor function".

ceiling function

$\lceil x \rceil$

\lceil x \rceil

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They come from "ceiling function".

Gaussian brackets sample

$\begin{eqnarray} [x] = \lfloor x \rfloor = \max\{ n\in\mathbb{Z} \mid n \leqq x \} \end{eqnarray}$

\begin{eqnarray}
[x]
= \lfloor x \rfloor
= \max\{ n\in\mathbb{Z} \mid n \leqq x \}
\end{eqnarray}

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The definition of the Gaussian brackets.