This principle is not a generalization of the pigeonhole principle for finite sets however : It is in general false for finite sets.
22.
With Yakir Aharonov and his group, Popescu discovered a number of quantum paradoxes, such as the quantum Cheshire Cat, and the quantum pigeonhole principle.
23.
:Your argument uses the basic version of the pigeonhole principle, but there's also a talk ) 19 : 36, 15 September 2008 ( UTC)
24.
Yes, the compressed string is longer than the uncompressed string; that's unavoidable in general ( by the pigeonhole principle, aka the counting argument ).
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In mathematics, the "'pigeonhole principle "'states that if items are put into containers, with, then at least one container must contain more than one item.
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Any reversible gate that consumes its inputs and allows all input computations must have no more input bits than output bits, by the pigeonhole principle.
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He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem.
28.
Invoking the pigeonhole principle doesn't seem to be the most natural way to explain this . talk ) 08 : 48, 6 August 2008 ( UTC)
29.
There are 5 edges incident to " v " and so ( by the pigeonhole principle ) at least 3 of them must be the same colour.
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Another way to phrase the pigeonhole principle for finite sets is similar to the principle that finite sets are Dedekind finite : Let and be finite sets.
