one-to-one correspondence

one-to-one correspondence
Two sets can be put into one-to-one correspondence when to each element of one there corresponds one element of the other, and to each distinct element of the one a different element of the other. Counting is an operation that puts n-membered sets of objects into one-to-one correspondence with the set of the first n natural numbers. When two sets can be put into such a correspondence they are equinumerous.
This definition makes no use of numbers, and opens the way to defining a number in terms of a set of equinumerous sets. It thus lies at the heart of the logicist programme of Frege and Russell . See also Hume's principle.

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • One-to-one — or one to one may refer to: One to one function or injective function One to one correspondence or bijective function One to one (communication), the act of an individual communicating with another One to one computing, an initiative for a… …   Wikipedia

  • One-to-one (disambiguation) — One to one or one to one is an adjective which can qualify: *in mathematics, an injective function (one to one) or a bijective function (one to one correspondence) *in telecommunications, one to one (communication) *in computer science, one to… …   Wikipedia

  • one-on-one — I adjective 1. directly between two individuals one on one instruction • Similar to: ↑private 2. being a system of play in which an individual defensive player guards an individual offensive player one on one defense • Syn: ↑ …   Useful english dictionary

  • one-for-one — | ̷ ̷ ̷ ̷| ̷ ̷ adjective : one to one a one for one correspondence between symbols and syllables Kenneth Croft * * * one for one «WUHN fuhr WUHN», adjective. = one to one. (Cf. ↑one to one) * * * denoting or referring to a situation or… …   Useful english dictionary

  • one-to-one — adj 1.) between only two people ▪ tuition on a one to one basis 2.) matching each other exactly ▪ a one to one correspondence between letters and sounds >one to one adv ▪ I need to discuss it with him one to one …   Dictionary of contemporary English

  • one-to-one — [wun΄tə wun′] adj. 1. permitting the pairing of an element of one group with a corresponding element of another group 2. Math. designating a correspondence such that each member of a set has just one partner in another set, and no element in… …   English World dictionary

  • one-to-one — correspondence …   Philosophy dictionary

  • one-to-one correspondence — abipusė atitiktis statusas T sritis fizika atitikmenys: angl. one to one correspondence vok. gegenseitige Korrespondenz, f rus. взаимное соответствие, n pranc. correspondance biunivoque, f …   Fizikos terminų žodynas

  • one-to-one — adj. One to one is used with these nouns: ↑correspondence, ↑discussion, ↑interview, ↑marketing, ↑relationship, ↑session, ↑teaching, ↑training, ↑tuition …   Collocations dictionary

  • one to one correspondence — direct correspondence in which every item has exactly one counterpart …   English contemporary dictionary

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