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/baɪˈd͡ʒɛk.ʃən/ · noun
(set theory) A one-to-one correspondence, a function which is both a surjection and an injection..
The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.
Note in particular that a function is a bijection if and only if it's both an injection and a surjection.
The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.
Use bijection when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Bijection means (set theory) A one-to-one correspondence, a function which is both a surjection and an injection..
Common synonyms include bijective function, one-to-one correspondence.
The opposite depends on the specific sense.
The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.
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