Injective, Surjective, And Bijective

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Definition (Injective, Surjective, And Bijective)

Let $D$ and $R$ be sets and let $f$ be a function from $D$ into $R$, so we have $f:D\to R$.

• We say that $f$ is injective (or one-to-one) if and only if for every $a,b\in D$ we have $f(a)=f(b)$ implies $a=b$.
• We say that $f$ is surjective (or onto) if and only if for every $y\in R$ there exists an $x\in D$ such that $y=f(x)$.
• We say that $f$ is bijective if and only if the function $f$ is both injective and surjective.