Editing Set (mathematics) (section)

{{about|sets themselves|the branches of mathematics studying sets|Naive set theory|and|Set theory}}
{{Short description|Collection of mathematical objects}}
[[File:Example of a set.svg|thumb|A set of polygons in an [[Euler diagram]]]]
[[File:Example of a set rearranged.svg|thumb|This set equals the one depicted above since both have the very same elements.]]

In [[mathematics]], a '''set''' is a collection of different things; these things are called ''[[Element (mathematics)|elements]]'' or ''members'' of the set and are typically [[mathematical object]]s of any kind: numbers, symbols, points in space, lines, other [[geometric shape]]s, variables, or even other sets.  A set may be [[finite set|finite]] or [[infinite set|infinite]], depending whether the number of its elements is finite or not. There is a unique set with no elements, called the [[empty set]]; a set with a single element is a [[singleton (mathematics)|singleton]].  

Sets are ubiquitous in modern mathematics. Indeed, [[set theory]], more specifically [[Zermelo–Fraenkel set theory]], has been the standard way to provide rigorous [[foundations of mathematics|foundations]] for all branches of mathematics since the first half of the 20th century.