Element (mathematics)
Sets

Writing A = { 1, 2, 3, 4 } {\displaystyle A=\{1,2,3,4\}} means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example { 1, 2 } {\displaystyle \{1,2\}}, are subsets of A.

Sets can themselves be elements. For example, consider the set B = { 1, 2, { 3, 4 } } {\displaystyle B=\{1,2,\{3,4\}\}}. The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set { 3, 4 } {\displaystyle \{3,4\}}.

The elements of a set can be anything. For example, C = { r e d, g r e e n, b l u e } {\displaystyle C=\{\mathrm {\color {Red}red},\mathrm {\color {green}green},\mathrm {\color {blue}blue} \}} is the set whose elements are the colors red, green and blue.

In logical terms, (x ∈ y) ↔ (∀ x : x ∈ 𝔇 y).
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