/sci/ - Science & Math

>>9060684
Define 1 such that [math]1*x = x \ \forall \ x[/math]
Now define 0 such that [math]0*x = 0 \ \forall \ x[/math]

If [math]1 = 0[/math] then necessarily [math]x = 0 \ \forall \ x[/math]
So the existence of a single nonzero number x would contradict the assertion that 1=0.

But alas, I don't know how to prove the existence of a number whose only property is that it's not zero, especially when operating under the assumption that 1=0, which implies that every number is zero. How can I prove that at least one number is not zero when I've made an assumption that implies ALL numbers are zero?

I'm thinking this is one of those "unprovable but true statements" Godel was going on about...