Proper Subset

A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is therefore a proper subset of any nonempty set.

For example, consider a set {1,2,3,4,5}. Then {1,2,4} and {1} are proper subsets, while {1,2,6} and {1,2,3,4,5} are not.

See also

Improper Subset, Set, Subset

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Kamke, E. Theory of Sets. New York: Dover, p. 6, 1950.

Referenced on Wolfram|Alpha

Proper Subset

Cite this as:

Weisstein, Eric W. "Proper Subset." From MathWorld--A Wolfram Web Resource.

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