injective function

$\text{[math]}$ is called injective if for every $\text{[math]}$ if $\text{[math]}$ then $\text{[math]}$
or, for every $\text{[math]}$ if $\text{[math]}$ then $\text{[math]}$

a function $\text{[math]}$ is one-to-one (or injective) if different elements map to different elements:
$\text{[math]}$ equivalently, a function is one-to-one if
$\text{[math]}$ [cite:;taken from @tao_analysis_1 definition 3.3.17]