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.’
    • ‘Rabh's proof defines a bijection between a disk and a triangle.’
    • ‘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.’
    • ‘In fact, it is easy to see that this bijection provides a conjugacy.’