In mathematics, (in general) what we mean by identification between two things? Shoud we find a bijection between the sets that we take this thing? or it is something else, if so please explain.
2026-04-09 14:30:14.1775745014
Identification in general
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In general the term "isomorphism" is used to denote "things" which are identical in respect of the particular mathematical properties of interest in the particular case.
So isomorphic groups have the same cardinality (bijection) but also behave the same way under the group operation.
There are other terms used eg in topology "homeomorphic" - this refers not just to the "things" but the fact also that the bijection is continuous both ways - so sometimes the properties of the maps/functions between things are important as well as the things themselves.
In each field of (pure) mathematics the question "when are two objects to be treated as essentially the same" is one of the key questions, and is answered in relation to the particular properties of interest in that field.