Element of

The left-hand item is a member of the right-hand set.

A set is a collection of things, written inside curly braces. 3 ∈ {1, 2, 3} says that 3 is one of that set's members. Read it aloud as "is in", "belongs to" or "is an element of". The order matters: the member goes on the left and the set on the right. To write the same fact the other way round, use ∋ ("contains as member"): {1, 2, 3} ∋ 3.

The Italian mathematician Giuseppe Peano introduced the sign in 1889, in his book on the foundations of arithmetic. His mark was an epsilon, the first letter of the Greek word ἐστί, meaning "is". Later typesetting turned it into the rounded, stylized ∈ used today.

∈ is not epsilon and not subset

Epsilon is a letter. ∈ is a relation between an item and a set. The Greek letter ε or ϵ names a quantity, such as "a small positive number" in calculus. ∈ only ever links an item to a set. Unicode encodes them as different characters, so search, screen readers and equation software treat them differently.

Use ∈ only for single members. When the left-hand side is itself a set that sits inside another set, you need a subset sign such as ⊆: {1} ⊆ {1, 2}, while 1 ∈ {1, 2}. For "not a member", the crossed form is ∉: x ∉ A.

How do I type ∈?

Type \in in LaTeX math mode, or ∈ in HTML.

LaTeX is the typesetting system used for most maths papers, and \in is one of its basic commands. In a web page, ∈ or ∈ displays the sign. Equation editors such as the ones in Word or Google Docs accept \in too, or list the sign among relation symbols.