hello,

I was wondering if I could have some help with this problem; there is a list of properties on the natural numbers that the problem asks us to reference and use at our own discretion. However, I’m not entirely sure which properties I should use to prove the following by induction, after having shown the base case. I’m having most trouble showing the inductive case, i.e. the n+1 case.

Let f : N → N be a function. Suppose that f(n)< f(n+1) for all n∈N. Prove that f(n)≥n for all n∈N.

Thank you for your help

All the best

 

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