Bijection

• Definition: A bijection is a function $f:A\to B$ that is both injective and surjective.
• Meaning: Every element in $A$ maps to a unique element in $B$, and every element in $B$ is covered.
• Notation: Sometimes written $A\leftrightarrow B$ or expressed by saying ”$f$ is a bijection.”
• Example: the function $f(x)=x+1$ from $\mathbb{Z}\to \mathbb{Z}$ is bijective.