Math Memorabilia

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philosophy/math math-definitions

Q: What is the difference between a bijection and an isomorphism?

A: An isomorphism is a bijection that also preserves structure.

• If we take two copies of the integers and map every number in the first one to itself in the second, except we send 5 to 10 and 10 to 5, this is a bijection since we’ve made a 1-1 correspondence, but isn’t an isomorphism since things like order and addition and multiplication are not preserved in general (7 < 10 but f(7) > f(10))

• https://old.reddit.com/r/math/comments/7bdyui/isomorphic_and_bijective_are_the_same_thing/

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Cloze

A {{c2::morphism}} can be considered a slightly more abstract, not necessarily structure preserving version of a {{c1::homomorphism}}.

Back Extra: (these are my own words, take with a grain of salt)

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