

Wolfram Alpha proves that N = N - 1 - uninverted
http://www.wolframalpha.com/input/?i=((n%2Fn)+%3D%3D+(n-1)%2F(n-1))+%26%26+Implies[((a%2Fa)+%3D+(b%2Fb))%2C+(a+%3D+b)]+%26%26+Implies[((n%2Fn)+%3D%3D+((n-1)%2F(n-1)))+%26%26+Implies[(a%2Fa)+%3D%3D+(b%2Fb)%2C+(a+%3D%3D+b)]%2C+(n+%3D%3D+n+-+1)]+%26%26+Implies[n+%3D%3D+n+-+1%2C+1+%3D%3D+2]

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apotheon
. . . but you can't tell anyone about it except by linking to it, because
Wolfram Alpha copyrighted it.

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uninverted
This is _very_ dubious (proving the opposite is easier), but it was quite a
lot of fun.

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skermes
I can see how it may have been fun, but it doesn't even really rate as
dubious.

Not only is one of your premises (a/a = b/b -> a=b) clearly false, but your
conclusion doesn't mean anything.

a=b ^ a=b -> n=(n-1) ^ n!=(n-1) is just a contradiction. Your first and second
terms together imply n=(n-1) which directly contradicts your third term.

I'm afraid you've simply proved a contradiction, which just means (because of,
well, proof by contradiction) that you're arguments are flawed.

