Or is it a bijection that is everywhere defined ?
2026-04-12 22:55:28.1776034528
Is one-to-one correspondence the same as bijection?
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I believe there is a subtle difference between a bijection and a one-to-one-correspondence, especially in popular math treatments of set theory. The difference being that a one-to-one-correspondence between two sets is sometimes drawn with two-directional arrows that relate elements of the two sets. A bijection, being a mapping, is usually depicted with one-directional arrows or rays relating the elements. In the former case the distinction between the domain and range is not really meaningful, whilst in the latter case it is meaningful and we call the sets domain and co-domain respectively. It seems that according to wikipedia a one-to-one correspondence is a bijection, so one-directional arrows are appropriate. Though the distinction between rays and double sided arrows is not important since the inverse relation is also a bijection.
I am afraid we may just be splitting hairs here.