# One-to-One Correspondence

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## one-to-one correspondence

[¦wən tə ¦wən ‚kär·ə′spän·dəns]
(mathematics)
A pairing between two classes of elements whereby each element of either class is made to correspond to one and only one element of the other class.

## One-to-One Correspondence

in mathematics, the correspondence between elements of two sets such that each element of the first set corresponds to a specific element of the second set and each element of the second set corresponds to a specific element of the first set. A one-to-one correspondence is a particular form of a function or mapping, in which the given function and its inverse are single-valued. If a one-to-one correspondence can be established between two sets, then these sets are equivalent. For example, the sets of integers and their squares are equivalent since the correspondence n → n2 is a one-to-one correspondence.

References in periodicals archive ?
The simplicity of the one-to-one correspondence between the Federal Reserve's balance sheet and excess reserves hides the difficulty involved in predicting how banks are likely to behave in the presence of the expanded reserves.
The one-to-one correspondence between classical and quantum wave interpretation asserted here actually can be expected not only in the context of Feynman's derivation of Maxwell equations from Lorentz force, but also from known exact correspondence between commutation relation and Poisson bracket [3,6].
In 1873, the German mathematician Georg Cantor published a paper in the Crelle Journal which proved that the set R of the continuum of real numbers is non-denumerable; that is, there is no one-to-one correspondence from the set N to the set R.
Three types of children's quantitative notions were noted in the play, one-to-one correspondence, counting, and adding.
The first set of 'Beginning Activities' starts from the simple basics of checking for one-to-one correspondence, and that children understand the relationship between written and spoken words and the gaps between words on the page.
Although we read allegorical explanations of the parables in this week's gospel readings, a parable is not an allegory with a single interpretation and a one-to-one correspondence with the world.
On the simplest level, once Jean-Do's right eye is sewn shut (in an already famous scene that allows us to imagine the panic induced upon seeing a needle and thread pass though one's own eyelid), the one-to-one correspondence between the monocular vision of the camera and that of Jean-Do is made logically and dramatically appropriate.
In order to do this, he argues, the European Union must assume greater burdens in promoting a cohesive western economic and security strategy, it must also strive for greater one-to-one correspondence between the states of the North Atlantic Treaty Organization and the states of the Union and build up NATO's military forces, and it should form a strategic compact with the United States that helps restore the international legitimacy lost by the United States in the wake of its invasion of Iraq.
N emphasizes that it is not the case that there is simply 'a one-to-one correspondence of modes across attributes' (125) but rather 'a one-to-one correspondence between the modes of Thought (ideas), on the one hand, and, on the other hand, the modes of every attribute' (126).
Lincoln agrees with many scholars that the Fourth Gospel's truth claims about Jesus are inextricably tied to the context and struggle of the Johannine community as a "marginalized group" and that "it is not plausible to defend any consistent or detailed one-to-one correspondence between John's narrative and what is likely to have happened in the ministry of Jesus" (p.
She also investigates the meaning of the term after life before its appearance in art criticism, explaining how, in sixteenth-century natural history, after life was a label widely used to guarantee the one-to-one correspondence between an image and the specimen it represented: indeed, to make possible the substitution of the image for the thing itself.
Whereas once upon a time our industry's tried and true control packages consisted of long stories which truly sold the mission, or truly one-to-one correspondence which educated and informed, our mailboxes have become overrun with product and perfunctory billing statements.

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