proper inclusion en · NOUN
Meanings
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(uncountable) The state of being a proper subset; a subset relation in which a set A is a subset of a set B but A is not equal to B.
The symbol ⊆ is used for ordinary inclusion, and ⊂ is sometimes used for proper inclusion.
1960, Paul R. Halmos, Naive Set Theory, Van Nostrand, page 6: