Bifalgorithm post · Brisk · Chapter 1

What is a bijective function?

What is a bijective function? (Brisk · Chapter 1) — "A bijective function is simply one that is both injective and surjective. With an injective function, ever…

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  • A bijective function is both injective and surjective.
  • An injective function maps every y to at most one x.
  • A surjective function maps every y to at least one x.
  • Therefore, a bijective function maps every y to exactly one x.
  • The domain and codomain must have the same cardinality.
  • The employeeNumber function is a bijection.
  • Every employee has an employee number.
  • Every employee number corresponds to exactly one employee.
  • There are the same number of employees as employee numbers.
  • A bijective function is also called a bijection.
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What is a bijective function?

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Brisk

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"A bijective function is simply one that is both injective and surjective. With an injective function, every y is mapped to by at most one x; with a surjective function, every y is mapped to by at least one x; so with a bijective function, every y is mapped to by exactly one x. Needless to say, the domain and the codomain must have the same cardinality for this to be possible. The function employeeNumber—with employees as the domain and employee numbers as the codomain—is a bijective function. Every employee has an employee number, and every employee number goes with exactly one employee. As a corollary of this, there are the same number of employees as employee numbers. A bijective function is also called a bijection."

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