Non-empty

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Mainly to document my use of "non-empty in"

Grade: E

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Low priority, the "non-empty in" bit could even be my own term.... doesn't matter much

Definition

A set, [ilmath]A[/ilmath] is non-empty if:

• [ilmath]A\ne[/ilmath] [ilmath]\emptyset[/ilmath] - why am I even bothering to write this?

Non-empty in

Suppose [ilmath]A[/ilmath] and [ilmath]B[/ilmath] are sets. We say "[ilmath]A[/ilmath] is non-empty in [ilmath]B[/ilmath]" if:

• [ilmath]A\cap B\ne\emptyset[/ilmath] - literally, the part of [ilmath]A[/ilmath] that is in [ilmath]B[/ilmath] also is non-empty (see "disjoint in" also, "empty in" too)