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**Power Out** Just been looking at the proof a bit more, think I may have got somewhere.

We've assumed that P(m) is true for all m less than or equal to n, and n is greater than or equal to 0.

From this we got x^n=x^(n-1)=1.

If we choose n=0 then we're told to assume x^n=1. But n-1=-1, which isn't greater than or equal to 0. As such we can't assume that x^n-1=1.

Hence x^(n+1)= (x^n*x^n)/x^(n-1)=1.1/1=1 only when n is greater than or equal to 1. So the problem is getting between the base case and the n=1 step (one doesn't lead to the other).

This seems right as if you know x^1=1 it follows that x^2=x*x=1, x^3=x*x*x=1 and so on. But just knowing x^0=1 doesn't enable you to say x^1=1.

Does this sound along the right lines?