Editing Semicolon (section)

== Mathematics ==
In mathematical derivations, a semicolon is used to separate expressions in a sequence, similar to its use in spoken English, and may be considered either punctuation for the mathematical expressions, or as punctuation for the words spoken when reading the expressions. For example, [[completing the square]]:

::<math>~ \mathrm{~ Given ~}\; a x^2 + b x + c = 0 \quad \mathrm{~ and ~} \quad a \ne 0 \ ; </math>
::<math>\ \left[ x^2 + 2\ \frac{b}{\ 2a\ } x + \left( \frac{b}{\ 2a\ } \right)^2 \right] - \left( \frac{b}{\ 2a\ } \right)^2 + \frac{\ c\ }{a} = 0 \qquad \mathrm{~ for\ all ~}\; a \ne 0, ~~ \mathrm{~ and\ any ~}\; b, c \ ; </math>
::<math>\ \left[ x +  \frac{b}{\ 2a\ } \right]^2 = \left( \frac{b}{\ 2a\ } \right)^2  - \frac{\ c\ }{a} \ ; </math>
::<math>\ \Biggl| x + \frac{b}{\ 2a\ } \Biggr| = \sqrt{\  \left( \frac{b}{\ 2a\ } \right)^2  - \frac{\ c\ }{a} ~~} \qquad \mathrm{~ if ~}  \quad x + \frac{b}{\ 2a\ } \in \mathbb{R} \quad \mathrm{~ and ~} \quad \left( \frac{b}{\ 2a\ } \right)^2  - \frac{\ c\ }{a} \ge 0 ~.</math>

In the argument list of a mathematical [[function (mathematics)|function]] <math>\ f(x_1,\ x_2,\ \dots\ ;\ a_1,\ a_2,\ \dots) \; ,</math> a semicolon may be used to separate [[variable (mathematics)|variables]] from fixed [[parameter#Mathematical functions|parameters]].{{citation needed|date=December 2014}}

In [[differential geometry]] and [[tensor analysis]] a semicolon preceding an [[Indexed family|index]] is used to indicate the [[covariant derivative]] of a function with respect to the [[coordinate]] associated with that index.

In the [[calculus of relations]], the semicolon is used in [[infix notation]] for the [[composition of relations]]: <math>A;B \ =\ \{(x,z): \exists y \ \ xAy \ \land\ yBz \} ~.</math>

In [[piecewise functions]], a semicolon or comma may follow the subfunction or subdomain; the <math>\text{if}</math> or <math>\text{for}</math> can be omitted, in which case it seems replaced by the semicolon or comma.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Piecewise Function |url=https://mathworld.wolfram.com/PiecewiseFunction.html |access-date=2024-07-20 |website=mathworld.wolfram.com |language=en}}</ref>

The {{mono|1=;}} ''[[Humphrey point]]'' is sometimes used as the "[[decimal point]]" in [[duodecimal]] numbers: 54;6<sub>12</sub> equals 64.5<sub>10</sub>.