does f(n+1)>f(n) for all n prove injectivity?

[eternal coral]

pretty sure it does but just to confirm

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[paper escarp]

Depends how it’s defined

If f ∊ R^ Z then yes it is injective meaning that, the initial set is the set of negative and positive integers

But for example f(x)={x if x ∊Z, x^2 if not} satisfies these conditions and is not injective

f(-1/2)=f(1/2)=1/4

[timid plank]

No. See f(x) = floor(x) as a counterexample.

[eternal coral]

thanks!

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