Editing Sigma (section)

==== Mathematics ====
* In general mathematics, lowercase '''σ''' is commonly used to represent unknown angles, additionally serving as a shorthand for "[[countable set|countably]]", whereas '''Σ''' is regularly used as the [[operator (mathematics)|operator]] for [[summation]], e.g.:<ref name=":0">{{Cite web |last=Weisstein |first=Eric W. |title=Sigma |url=https://mathworld.wolfram.com/Sigma.html |access-date=2025-01-25 |website=mathworld.wolfram.com |language=en}}</ref>
<math display="block">\sum_{k=0}^5k= 0 + 1 + 2 + 3 + 4 + 5 = 15</math>
* In [[mathematical logic]], <math>\Sigma^0_n</math> is used to denote the set of formulae with bounded quantifiers beginning with existential quantifiers, alternating <math>n-1</math> times between existential and universal quantifiers. This notation reflects an indirect analogy between the relationship of summation and products on one hand, and existential and universal quantifiers on the other. See the article on the [[arithmetic hierarchy]].
* In [[statistics]], '''σ''' represents the [[standard deviation]] of population or [[probability distribution]] (where [[Mu (letter)|mu]] or '''μ''' is used for the mean).<ref name=":0" />
* In [[topology]], '''σ-compact''' [[topological space]] is one that can be written as a countable [[union (set theory)|union]] of [[compact space|compact subsets]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Sigma-Compact Topological Space |url=https://mathworld.wolfram.com/Sigma-CompactTopologicalSpace.html |access-date=2025-01-25 |website=mathworld.wolfram.com |language=en}}</ref>
* In [[mathematical analysis]] and in [[probability theory]], there is a type of [[Field of sets|algebra of sets]] known as '''[[sigma-algebra|σ-algebra]]''' (aka '''σ-field'''). Sigma algebra also includes terms such as:
** '''σ(''A'')''', denoting the [[Σ-algebra#σ-algebras generated by families of sets|generated sigma-algebra]] of a set ''A''
** '''[[Σ-finite measure]]''' (see [[Measure (mathematics)|measure theory]])
* In [[number theory]], '''σ''' is included in various [[divisor function]]s, especially the '''sigma function''' or sum-of-divisors function.
* In [[applied mathematics]], '''σ(''T'')''' denotes the spectrum of a [[linear map]] ''T''.
* In [[complex analysis]], '''σ''' is used in the [[Weierstrass functions#Weierstrass sigma-function|Weierstrass sigma-function]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Weierstrass Sigma Function |url=https://mathworld.wolfram.com/WeierstrassSigmaFunction.html |access-date=2025-01-25 |website=mathworld.wolfram.com |language=en}}</ref>
* In [[probability theory]] and [[statistics]], '''Σ''' denotes the [[covariance matrix]] of a set of [[random variable]]s, sometimes in the form <math>\;|\!\!\!\Sigma</math> to distinguish it from the summation operator.
* [[Spectral theory|Theoretical spectral analysis]] uses '''σ''' as standard deviation opposed to lowercase [[Mu (letter)|mu]] as the absolute mean value.