4.4.  Membership

For any set S and any object x, either x is a member of S or it is not.

In order to indicate that x is a member of S, we write x ∈ S
x ∈ S is a shorthand for: x is a member of S.

In order to indicate that x is not a member of S, we write x ∉ S
x ∉ S is a shorthand for: x is not a member of S.

Examples: The following are true statements

• 2 ∈ { 2, 3, 4 }
• hp ∉ { w | w is a string of n letters, where n = 4 }
• P = { n | n is a natural number divisible by exactly two natural numbers }
  3 ∈ P
• S1 = { 1, 11 }
  S2 = { 2, 22 }
  S3 = { 3, 33 }
  S4 = { 1 }
  S = { S1, S2, S3 } = { { 1, 11 }, { 2, 22 }, { 3, 33 } }
  S1 ∈ S
  S4 ∉ S

Last modified 22/May/97