Bijection

A function that is both injective and surjective — a one-to-one correspondence between two sets.

Definition

A function \(f: A \to B\) is a bijection if: 1. It is injective (one-to-one): \(f(x) = f(y) \Rightarrow x = y\) 2. It is surjective (onto): \(\forall b \in B, \exists a \in A: f(a) = b\)

Properties

• A bijection has an inverse function \(f^{-1}: B \to A\)
• Two sets have the same cardinality if and only if there exists a bijection between them

Example

To be written.

Related Concepts

• Function
• Injection
• Surjection
• Inverse Function