vault backup: 2026-03-09 23:52:22
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@@ -84,3 +84,8 @@ A := {1, 2, 3} \
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cal(P)(A) = {emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
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$$
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## Closures
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A **closed set** under the binary operation $*$ denoted by $forall a,b in S, a * b in S$
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"All $a * b$ from set $S$ are included in set $S$"
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A set can be closed under any binary operation ($+, -, *, \/$), depending on the set itself if it actually is closed or not. $NN$ for example is not closed under subtraction.
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