Re:Code is run more than read
by denotational on Friday December 01, 2023 @06:28AM
(#38485590)
> It isn't useful in mathematics because it is a contradiction in terms: if "neither of the two compared entities is greater or lesser than the other" then they are equal.
That’s only true for a total order; there are many interesting orders that do not have this property.
It holds for the usual ordering on N, Z, Q and R, but it doesn’t hold for more general partially ordered sets.
In general one has to prove that an order is total, and this is frequently non-trivial: Cantor-Schröder-Bernstein can be seen as a proof that the cardinal numbers have a total order.
Re:Code is run more than read
by adastra22 on Friday December 01, 2023 @06:35AM
(#38485640)
Example: alphabetic ordering in most languages with diacritics. For example, "ea" < "éz", but also "éa" < "ez". That's because e and é are treated the same as far as the ordering function is concerned, but they are obviously also NOT the same glyph.
That’s only true for a total order; there are many interesting orders that do not have this property.
It holds for the usual ordering on N, Z, Q and R, but it doesn’t hold for more general partially ordered sets.
In general one has to prove that an order is total, and this is frequently non-trivial: Cantor-Schröder-Bernstein can be seen as a proof that the cardinal numbers have a total order.