March 28th, 2018, 06:33 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 275 Thanks: 32  Function proof
If $\displaystyle f(n+1)> f(f(n))$ Show that $\displaystyle f(n)=n$ 
March 28th, 2018, 07:13 AM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,921 Thanks: 774 Math Focus: Wibbly wobbly timeywimey stuff.  
March 28th, 2018, 08:00 AM  #3 
Senior Member Joined: Aug 2017 From: United Kingdom Posts: 284 Thanks: 86 Math Focus: Algebraic Number Theory, Arithmetic Geometry 
I'm assuming this is meant to be a function $\mathbb{N} \to \mathbb{N}$. Have you tried anything so far? With most maths problems, and this sort of problem especially, there's very little to gain from seeing someone else's solution without having a proper go at it yourself. I'll give one hint for now. With these problems, it often helps to think about certain special values of the function. For example, you could try firstly to prove that $f(0) = 0$ (or, if $0$ isn't an element of $\mathbb{N}$ for you, that $f(1) = 1$). 

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