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Xuanwu
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Homework Statement
For any given n, where n is an element of the natural number set, prove n^2 > n +1, for all n > 1.
Homework Equations
This week in lecture we defined the greater than relationship as:
Let S = Natural numbers
Let R = {(a,b): [itex]\exists[/itex] c: a = b+c}
then aRb
The Attempt at a Solution
My first thought was show a general expression of either an odd of even number (n = 2x + 1 or n = 2x), but the resultant (4x^2 + 4x +1 > 2x + 2 and 4x^2 > 2x +1 for odd/even respectively) doesn't really give me anything useful as far as I can see.
I can see that it would be true, as n = 2 would be 4 > 3, and n= 3 would be 9 > 4, I'm just not sure on how to get started.
Some literature on approaches to getting started on proofs would be great, as I find I'm fairly hit/miss. I can either see the approach or I stand there going "I know it's true, but I can't show it's true".
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