Math 2.0

definition

Injective function

Definition

Let f ⁣:A→Bf \colon A \to B be a function. The function ff is injective when, for all a,a′∈Aa, a' \in A, f(a)=f(a′)f(a) = f(a') implies a=a′a = a'.

Remarks

Other names are one-to-one function and injection. The function x↦2xx \mapsto 2x on R\mathbb{R} is injective, and x↦x2x \mapsto x^2 on R\mathbb{R} is not, because f(1)=f(−1)f(1) = f(-1). An injective function with a nonempty domain has a left inverse. See injective iff it has a left inverse.

Explanations

L1 human

An injective function never sends two inputs to the same place. To prove injectivity, assume f(a)=f(a′)f(a) = f(a') and deduce a=a′a = a'.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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Sources

  1. Web https://en.wikipedia.org/wiki/Injective_function, lead section

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