One-to-One Function

A function is said to be one-to-one if each element of the range is associated with exactly one element of the domain. Two different elements in the domain (A) have different images in the co-domain (B).

a₁ ≠ a₂ ⇒ f(a₁) ≠ f(a₂); a₁, a₂ ∈ A

f(a₁) = f(a₂) ⇒ a₁ = a₂

A function is said to be injective if it is one-to-one. It is said to be bijective if it is both one-to-one and onto.