Something for candidates to think about... about

siavosh

Simple proof:
     No Study = Fail
+  Study = No Fail
     No Study + Study = No Fail + Fail
     (No + 1) Study = (No + 1) Fail
     (No + 1) Study = (No + 1) Fail
     Study = Fail

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.

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.

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.

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.

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.

needhelp1700

You absolutely can add exclusive events, and in fact, we use the fact that we can very often to solve problems. Tautology: You will either study or not study. Probability identity: P(study) + P(not study) = 1. And so on. Also, in response to your response to my third item: GFY

whew1110

BS. This example is not a tautology. Only a self referential statement. If I am, I am not= I am not. Unless I am. Logic 101. Or if p true, not p is false and (p and not p) is false (STILL cannot study and not study at he same time) P(study) + P( not study)= 1 is irrelevant. What’s relevant is P(study) * P( not study)= 0. Therefore, if study implies pass and not study fail,and both statements are true, not study cannot imply pass, because it means that study and not study are true at the same time.
3. You are most welcome.

Londonrocks

If you’re so good at logic, why do you think that adding events is the same thing as claiming two events occur simultaneously? Go back to “logic 101.” And my probability identity is not irrelevant. But what do I know? Those 40 math credits must have been wasted on me.

genuinecfa

I had no idea this would be so controversial