Subset

set whose elements are all contained in another set

In set theory, a set is called a subset of a set if all of the elements of are contained in . For example, any set is a subset of itself. Another example of a subset is a proper subset: a set is called a proper subset of a set if is subset of but is not equal to .

A is a subset of B.

The symbol "" always means "is a subset of."[1][2][3] The symbol "" always means "is a proper subset of." There is also the symbol "", which some authors use to mean "is a subset of"[4] and other authors only use to mean "is a proper subset of."[1]

For example:

  • is a subset of , so we could write .
  • is a proper subset of , so we could write ,, or .
  • The interval [0, 1] is a proper subset of the set of real numbers , so .
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References

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  1. 1.0 1.1 "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-08-23.
  2. Weisstein, Eric W. "Subset". mathworld.wolfram.com. Retrieved 2020-08-23.
  3. "Introduction to Sets". www.mathsisfun.com. Retrieved 2020-08-23.
  4. Rudin, Walter (1987), Real and complex analysis (3rd ed.), New York: McGraw-Hill, p. 6, ISBN 978-0-07-054234-1, MR 0924157