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)
Ranked by relevance and common usage.
Closest matches (1)
Noun(1 words)
Strong matches (1)
Related words (1)
Noun(1 words)
Related word relations
OpenGloss and ConceptNet supply richer edges like generalizations, collocations, and derivations.
Synonyms
1 entriesRelated terms
2 entrieshas context
1 entriesis a
1 entriesrelated to
4 entriesTranslations
36 translations across 26 languages.
Bulgarian
1 entries- биекция noun (function that is both a surjection and an injection)
Catalan
2 entries- bijecció noun (function that is both a surjection and an injection)
- funció bijectiva noun (function that is both a surjection and an injection)
Chinese Mandarin
2 entries- 一一映射 noun (function that is both a surjection and an injection)
- 雙射 /双射 noun (function that is both a surjection and an injection)
Czech
1 entries- bijekce noun (function that is both a surjection and an injection)
Dutch
1 entries- bijectie noun (function that is both a surjection and an injection)
Esperanto
3 entries- bijekcio noun (function that is both a surjection and an injection)
- dissurĵeto noun (function that is both a surjection and an injection)
- inversigebla funkcio noun (function that is both a surjection and an injection)
Estonian
1 entries- bijektsioon noun (function that is both a surjection and an injection)
Finnish
1 entries- bijektio noun (function that is both a surjection and an injection)
French
1 entries- bijection noun (function that is both a surjection and an injection)
German
2 entries- Bijektion noun (function that is both a surjection and an injection)
- bijektive Funktion noun (function that is both a surjection and an injection)
Greek
1 entries- αμφιμονοσήμαντη αντιστοιχία noun (function that is both a surjection and an injection)
Hebrew
1 entries- פונקציה חד־חד־ערכית ועל noun (function that is both a surjection and an injection)
Hindi
1 entries- एकैकी आच्छादन noun (function that is both a surjection and an injection)
Hungarian
2 entries- bijekció noun (function that is both a surjection and an injection)
- kölcsönösen egyértelmű leképezés noun (function that is both a surjection and an injection)
Icelandic
1 entries- gagntæk vörpun noun (function that is both a surjection and an injection)
Ido
1 entries- bijekto noun (function that is both a surjection and an injection)
Japanese
2 entries- 全単射 noun (function that is both a surjection and an injection)
- 双射 noun (function that is both a surjection and an injection)
Korean
1 entries- 전단사 noun (function that is both a surjection and an injection)
Polish
2 entries- bijekcja noun (function that is both a surjection and an injection)
- funkcja wzajemnie jednoznaczna noun (function that is both a surjection and an injection)
Portuguese
1 entries- bijeção noun (function that is both a surjection and an injection)
Romanian
2 entries- bijecție noun (function that is both a surjection and an injection)
- funcție bijectivă noun (function that is both a surjection and an injection)
Russian
1 entries- бие́кция noun (function that is both a surjection and an injection)
Serbo-Croatian
2 entries- bijekcija noun (function that is both a surjection and an injection)
- бијекција noun (function that is both a surjection and an injection)
Spanish
1 entries- biyección noun (function that is both a surjection and an injection)
Swedish
1 entries- bijektion noun (function that is both a surjection and an injection)
Vietnamese
1 entries- song ánh noun (function that is both a surjection and an injection)
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
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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.