A
function [math]f : A \href{/cs2800/wiki/index.php/%5Cto}{\to} B
[/math] is
injective if,
for all [math]x_1
[/math] and
[math]x_2 \href{/cs2800/wiki/index.php/%5Cin}{\in} A
[/math],
whenever [math]f(x_1) = f(x_2)
[/math], we have
[math]x_1 = x_2
[/math].
one-to-one is a synonym for
injective.
A good way of thinking about injectivity is that the domain is "injected" into the codomain without being "compressed". In other words, no two (different) inputs go to the same output.
The following function is not injective:
because [math]f(b)
[/math] and [math]f(c)
[/math] are both 2 (but [math]b \neq c
[/math]).
