Element of symbol (∈)

How to read it

OpenStax’s Contemporary Mathematics reads ∈ as “is a member of” and ∉ as “is not a member of”. Oscar Levin’s Discrete Mathematics gives the examples 2 ∈ {1, 2, 3}, since 2 is one of the elements listed, and 4 ∉ {1, 2, 3}. Written the other way round, A ∋ x, the reversed sign means “contains as a member” (Unicode, CONTAINS AS MEMBER, U+220B). NIST’s Digital Library of Mathematical Functions lists ∈ and ∉ in its common notations, and Unicode encodes them as ELEMENT OF (U+2208) and NOT AN ELEMENT OF (U+2209).

Also searched as: ∈, ∉, belongs to symbol, epsilon symbol in sets, is an element of, member of symbol, not an element of.

Element of or subset of?

The commonest mix-up is between ∈ and ⊆. Levin’s example: if A = {1, b, {x, y, z}, ∅} and B = {1, b}, every element of B is in A, but B itself is not one of A’s four elements, so B ∉ A. B is a subset of A, B ⊆ A, which Levin calls something different from being an element. ∈ relates a member to a set; ⊆ relates a set to a set.

Look-alikes

∈ is not the Greek letter epsilon ε, though it grew out of one. Unicode encodes a smaller form, ∊ SMALL ELEMENT OF (U+220A), which it says comes from mathematical fonts and is not the straight epsilon ϵ (U+03F5). In logic, the backwards ∃ means “there exists”.