Injectivity, Surjectivity, Bijectivity

• Injectivity, Surjectivity, Bijectivity #Card
  • A map $f : X \to Y$ is: - Surjective (onto) if $f(X) := {f(x) : x \in X} = Y$. - Injective (one-to-one) if $x_0 \neq x_1 \implies f(x_0) \neq f(x_1)$. - Bijective if it is both surjective and injective.

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A map $f : X \to Y$ is:

• Surjective (onto) if $f(X) := {f(x) : x \in X} = Y$.
• Injective (one-to-one) if $x_0 \neq x_1 \implies f(x_0) \neq f(x_1)$.
• Bijective if it is both surjective and injective.

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Function.Injective / Function.Surjective / Function.Bijective