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Jan Meyer
2026-03-07 09:46:32 +01:00
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9
DAS/Set Theory.md
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@@ -84,12 +84,3 @@ A := {1, 2, 3} \
cal(P)(A) = {emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
$$
## Relations
| Relation | Explanation | Example |
| ---------------- | :-------------------------------------------------------------------------------------------------------------------- | ------------------------- |
| *transitive*<br> | "chain reaction", a information about $a$ in relation to $c$ can be inferred from the relations $a -> b$ and $b -> c$ | $a < b, b < c => a < c$ |
| *reflexive* | every element is related to itself with the given relation | $a <= a, 5 = 5$ |
| *anti-reflexive* | every element is *NOT* related to itself in the given relation | $a < a$ |
| *symmetric* | the given relation work both ways | $a = b => b = a$ |
| *antisymmetric* | the given relation only works both ways if $a$ and $b$ are the same | $a <= b, b <= a => a = b$ |