The correct proof would be proof by induction (ya, it's hard to do for tautologies) :o
Statement: (-1)(x)<0 for all x>0 (for sanity's sake we'll just say x is also a whole number. Repeating decimals and proofs almost always do NOT mix
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Base case: x=1. (-1)(1)<0 goes to -1<0 I would believe this to be CORRECT :D
Induction: If x is assumed to be true within the currently defined subset of x>0, x+1 must also be proven true (domino theory). So, making a blind assumption that the statement (-1)(x)<0 reducing to -x<0 is correct, then I have to show that the statement of (-1)(x+1)<0 is correct. This reduces to -x<1. Because values for x can only be positive integers, the statement -x<1 is correct. Because it's correct, it shows that for every x that is true, x+1 is also true.
Here's what I did: it's called the domino theory. I had to prove that I knocked over the first domino (x=1) and prove that every domino knocks over the domino after it (prove for every x, x+1 is also true), which pretty much covers every possibility.
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