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Proper Subset

المؤلف:  Kamke, E

المصدر:  Theory of Sets. New York: Dover

الجزء والصفحة:  p. 6,

17-1-2022

3498

Proper Subset

 

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

For example, consider a set {1,2,3,4,5}" src="https://mathworld.wolfram.com/images/equations/ProperSubset/Inline6.svg" style="height:22px; width:106px" />. Then {1,2,4}" src="https://mathworld.wolfram.com/images/equations/ProperSubset/Inline7.svg" style="height:22px; width:64px" /> and {1}" src="https://mathworld.wolfram.com/images/equations/ProperSubset/Inline8.svg" style="height:22px; width:22px" /> are proper subsets, while {1,2,6}" src="https://mathworld.wolfram.com/images/equations/ProperSubset/Inline9.svg" style="height:22px; width:64px" /> and {1,2,3,4,5}" src="https://mathworld.wolfram.com/images/equations/ProperSubset/Inline10.svg" style="height:22px; width:106px" /> are not.

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REFERENCES

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