标题: Something for candidates to think about... [打印本页] 作者: siavosh 时间: 2013-4-21 18:19 标题: Something for candidates to think about...
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作者: noel 时间: 2013-4-21 18:24
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.作者: dontknow1987 时间: 2013-4-21 18:34
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.作者: skycfa 时间: 2013-4-21 18:38
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.作者: infinitybenzo 时间: 2013-4-21 18:39
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.作者: Matori 时间: 2013-4-21 18:51
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.作者: needhelp1700 时间: 2013-4-21 18:53
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 作者: whew1110 时间: 2013-4-21 18:55
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.作者: Londonrocks 时间: 2013-4-21 18:57
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.作者: genuinecfa 时间: 2013-4-21 18:58
I had no idea this would be so controversial作者: Penny-wenny 时间: 2013-4-21 19:04
Black Swan wrote:
I was just joking, thought it was a humorous feaux proof.
I’m just teasing you.作者: pacmandefense 时间: 2013-4-21 19:06
Good point. And you are right. Nevertheless, the proposed conclusion at the beginnig of this absurd topis is flawed. Let me put it this way, you cannot add two exclusive events and arrive at the proposed conclusion. No way. You are violating logic calculus rules, and, if for real, physics laws. All at the same time. To arrive at the proposed conclusion you have to assume that study and not study can occur at the same time, or are in fact the same thing. Which they cannot. So I restate, your probability identity is irrelevant here. And the conclusion reached is flawed and is not a tautology. A correct tautology would be (study implies pass) is identical to (notstudy implies fail). That’s it. You cannot reach the conclusion study implies fail, because you are ignoring the antecedent study implies pass. Wich, if assumed to be true, cannot be violated or you would be, in fact, assuming that study and notstudy are one and the same or concomitant at the least. So, yes, P(AB)=0 is relevant. Now, if you are going to try to prove otherwise, with your 40 credit maths courses and what not, go ahead.
Now, I know nothing of your academic background. I’m sure you worked your butt through college and I can certainly respect that. Whether the maths credits you took were wasted or not is your own problem. They aren’t proof that you are right and I’m wrong in this case, only that you took what appear to be advanced courses in college. Check that out in your logics handbook too.作者: rohitdoshi 时间: 2013-4-21 19:08
Except that this is a proof by algebra, and there are no conditional statements. The other cool thing about my academic background is that it taught me to tear down arguments in one sentence instead of huge paragraphs.作者: joemoran 时间: 2013-4-21 19:12
You’re really bad at this, for what it’s worth.
I’ll give you a hint so it doesn’t look like I can’t tear down your argument again: No Study != the NOT operator applied to “Study.”作者: cv4cfa 时间: 2013-4-21 19:13
Look, don’t hint and pretend you teared down anything. You either lay it out or you stay home. If I’m wrong I’ll own up to it. Also, FYI != means unequal not NOT operator. But whatever.
