A set is an unordered collection of objects. #### Notation A set with elements $a, b, c, \dots$ can be denoted as $\set{a,b,c,\dots}$, called Roster Notation. If the [[Set]] is large or [[Infinity|Infinite]],we can describe it using set-builder notation. $\huge \set{x \nonscript \mid \nonscript \mathopen{ P(x) }} $ Where $P(x)$ is some [[02 Areas/Math/Predicate|Predicate]] that $x$ must satisfy to be within the set. >[!example]- >$\huge >\set{2,4,6,\dots} = \set{ x \mid \mod(x,2) = 0 } >$ #### Membership The notation $x \in A$ means that the object $x$ is a member of the set $A$. #### Equality Two sets are equal if and only if they have the same elements. >[!example]- $ \set{1, 2, 3} = \set{4,2,1} $