Definition of bijection in English:
A mapping that is both one-to-one (an injection) and onto (a surjection), i.e. a function which relates each member of a set S (the domain) to a separate and distinct member of another set T (the range), where each member in T also has a corresponding member in S.
- Cantor had shown that there is a bijection between the interval [0,1] and the unit square but, shortly after, Netto had proved that such a bijection cannot be continuous.
- Often in combinatorics when an identity establishes the equality to two sets defined in different ways, one desires a bijection, namely, a one-to-one correspondence that converts members of one set to the other in a natural fashion.
- Rabh's proof defines a bijection between a disk and a triangle.
- Example sentences
- Due to the nature of the correction, the mapping is not bijective.
- Such a bijective proof of the Rogers-Ramanujan identities was found by Garsia and Milne by formulating an involution principle whose basic ideas can be traced to Schur's original combinatorial proof of these identities.
- The bijective part of the Bessel function yields the motion amplitude a.
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