Element of (∈) in LaTeX
\in typesets the set membership symbol ∈; means the object x is an element of the set A.
LaTeX command
\inNot the symbol you meant? Draw it to find the command →
Membership is the basic relation between an object and a set: says x is one of the things collected together in A. It is the workhorse symbol of set theory and appears everywhere quantifiers or set-builder notation are used, from defining domains of functions to stating hypotheses in a proof.
The most common mistake is mixing up \in with \subset. Membership links an element to a set (a point to a bag); subset links two sets to each other (a bag to a bigger bag). Write 2 \in \mathbb{N} but \mathbb{N} \subseteq \mathbb{Z}, never the other way round.
Negate membership with the dedicated \notin command rather than typing \not\in by hand; both render similarly in most engines but \notin has cleaner built-in spacing. The reversed relation \ni (, 'A contains ) is legal but rarely used outside a few stylistic contexts.
Other forms
\notinnot an element (∉)\nicontains (∋)Examples
$x \in \mathbb{R}$x is a real number
$n \in \mathbb{Z}$n is an integer
$\forall x \in S,\ x > 0$restricting a quantified variable to a set
$2 \notin \{1, 3, 5\}$negated membership
$\{x \in \mathbb{R} : x^2 < 4\}$set-builder notation using \in for the domain
Tips and common mistakes
- Do not confuse
\in(element of a set) with\subseteqor\subset(one set inside another); they are different relations with different meanings. - Use
\notinfor 'not an element of' rather than\not\in; it is the standard dedicated command. - In set-builder notation, put the
\inclause first: \{ : P(x)\}, so the reader knows the domain before the condition. \niis the mirror image of\in( means the same as ); use it sparingly, only when it reads more naturally in a sentence.- The blackboard-bold sets
\mathbb{R},\mathbb{Z},\mathbb{N},\mathbb{Q},\mathbb{C}are the most common right-hand side of\in.
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What is the difference between \in and \subset?
\in relates an element to a set ( means x is one of the things in A); \subset (or \subseteq) relates two sets to each other ( means every element of A is also in B). An element is not automatically a subset, and a subset is not an element, unless you are working with sets of sets.
How do I write 'not an element of' in LaTeX?
Use \notin, which renders as ∉. It works in any standard LaTeX or KaTeX math environment without extra packages.
Does \in need a package?
No. \in is a core TeX math symbol available in plain LaTeX and in KaTeX by default.
What is ∈ called?
It is usually read aloud as 'is an element of', 'belongs to', or 'in'; the symbol itself is called the membership sign or element-of sign.