Theorem: n=n+1
Proof: (n+1)^2 = n^2 + 2*n + 1
Bring 2n+1 to the left: (n+1)^2 - (2n+1) = n^2
Substract n(2n+1) from both sides and factoring, we have: (n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)
Adding 1/4(2n+1)^2 to both sides yields: (n+1)^2 - (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 - n(2n+1) + 1/4(2n+1)^2
This may be written: [ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2
Taking the square roots of both sides: (n+1) - 1/2(2n+1) = n - 1/2(2n+1)
Add 1/2(2n+1) to both sides: n+1 = n
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