Difference between revisions of "Non-empty"
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Latest revision as of 04:56, 1 October 2016
Stub grade: D
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Mainly to document my use of "non-empty in"
Grade: E
This page requires references, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.
The message provided is:
The message provided is:
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)
References
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