March 28th, 2018, 05:33 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 224 Thanks: 26  Function proof
If $\displaystyle f(n+1)> f(f(n))$ Show that $\displaystyle f(n)=n$ 
March 28th, 2018, 06:13 AM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,797 Thanks: 715 Math Focus: Wibbly wobbly timeywimey stuff.  
March 28th, 2018, 07:00 AM  #3 
Senior Member Joined: Aug 2017 From: United Kingdom Posts: 187 Thanks: 55 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 $f(1) = 1$). 

Tags 
function, proof 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Gama function times Zeta function proof  pedr0bessa  Abstract Algebra  0  July 11th, 2017 01:42 PM 
Transcendental Function Proof  millychoochoo  Number Theory  2  March 9th, 2014 08:21 AM 
Proof about Euler's ?function  page929  Number Theory  0  September 29th, 2010 09:29 AM 
Proof for a differentiable function  geyikrali  Real Analysis  2  July 19th, 2008 04:29 AM 
Proof about Euler's ?function  page929  Abstract Algebra  0  December 31st, 1969 04:00 PM 