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.
Source: wiktionary
Bijection
/baɪˈd͡ʒɛk.ʃən/
Synonyms for "bijection" (3 found)
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Closest matches (1)
Noun(1 words)
one to one correspondence
Strong matches (1)
Noun(1 words)
Related words (1)
Noun(1 words)
Sample sentences
3 total sentences available.
Note in particular that a function is a bijection if and only if it's both an injection and a surjection.
Source: wiktionary
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.
Source: wiktionary