Subset

set whose elements are all contained in another set From Wikipedia, the free encyclopedia

Subset
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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 .

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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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