Matori

1. You cannot add up two exclusive events. Cannot study and not study at the same time. First principle of thermodynamics applies.
2. Calling it an exercise in silly thinking is being very generous.
3. Good for you.

infinitybenzo

No, it proves that you can’t cancel, because when you do you lose the solution X = -1.
The whole point is that you can’t cancel when things are equal to 0, so if you cancel a (X + 1) term you ignore when X + 1 = 0 - X = -1.
Likewise, ohai’s statement is incorrect because (No + 1) = 0 might be a solution, so the proof is mathematically inconsistent if No = -1.
Imagine 6X = X. If you just divide by X, you get 6 = 1. However, you can’t do that, because the correct solution is 6X - X = X - X, which implies 5X = 0, so X = 0.

skycfa

aaronhotchner wrote:
Black Swan wrote:Are you sure? I mean, I’m not a math expert, but I feel like I’ve canceled (X+1)*X = (X+1) for a result of X=1 or similar equations many a time.
I’m positive. (X + 1) * X = (X + 1) implies X^2 + X = X + 1 which implies X^2 = 1. There are actually two solutions: X = -1 or X = 1, and by cancelling you completely ignored one of them. The same applies to your proof: it just assumes away possibilities that you aren’t allowed to do with deductive reasoning.
Actually, I solved the simplification incorrectly in that example (it is +-1, but I’m sure that arithmetically it’s correct now that you’ve said that. And that proves that you can in fact cancel that term when the outside term is a constant.

dontknow1987

Black Swan wrote:Are you sure? I mean, I’m not a math expert, but I feel like I’ve canceled (X+1)*X = (X+1) for a result of X=1 or similar equations many a time.
I’m positive. (X + 1) * X = (X + 1) implies X^2 + X = X + 1 which implies X^2 = 1. There are actually two solutions: X = -1 or X = 1, and by cancelling you completely ignored one of them. The same applies to your proof: it just assumes away possibilities that you aren’t allowed to do with deductive reasoning.

noel

You can’t assume it’s not, therefore you can’t cancel the terms. Study = Fail only when (No + 1) does not equal 0, but there is no evidence that it doesn’t. The logician in me weeps.