N equals N plus one.
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N equals N plus one


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

[Tag]:N equals N plus one
[Time]:5/9/2010
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