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Black Swan

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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
 
Black Swan wrote:
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
Click to expand...
(No + 1) = 0
you divided both sides by zero !
 
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.
 
Problem lies in the fact that
Study = No Fail
is not always infallibly true!
 
aaronhotchner wrote:
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.
Click to expand...
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.
 
“No” means “negative” or “minus”.
No Study = - Study = (-1) x Study
No + 1 = -1+1 = 0
you can not divide by zero
 
You can’t arbitrarily assign a value of -1 to No.
No if anything would best suited by 0, but isn’t meant to be a strictly numerical value. Arbitrarily saying it’s negative 1 would be like saying it’s 14*15 because N&O are the 14th and 15th letters of the alphabet.
 
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.
Click to expand...
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.
 
Well, the result is mathematically correct for any value of “No”…
(No)*Study = Fail
Study = (No)*Fail
is true for any value of “No”, so obviously, Study = Fail.
Though, I’m not sure if a term like (No)*Study has any meaning if “No” is an arbitrary variable. We could easily change “No” to “Yes” or “Maybe”, and the result would be the same.
 
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.
Click to expand...
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.
Click to expand...
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.
 
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.
 
ohai wrote:
Well, the result is mathematically correct for any value of “No”…
(No)*Study = Fail
Study = (No)*Fail
is true for any value of “No”, so obviously, Study = Fail.
Though, I’m not sure if a term like (No)*Study has any meaning if “No” is an arbitrary variable. We could easily change “No” to “Yes” or “Maybe”, and the result would be the same.
Click to expand...
the result is NOT correct mathematically for any value of “No”…
(No)*Study = Fail
AND
Study = (No)*Fail
is true ONLY for value of “No” = 1 or “No” = -1.
if “No” = 1 then
You have just assumed “Study = Fail” and you have not proved it.
if “No” = -1 then
You fail to prove “Study = Fail” when you divide by 0.
 
ohai wrote:
Well, the result is mathematically correct for any value of “No”…
(No)*Study = Fail
Study = (No)*Fail
is true for any value of “No”, so obviously, Study = Fail.
Though, I’m not sure if a term like (No)*Study has any meaning if “No” is an arbitrary variable. We could easily change “No” to “Yes” or “Maybe”, and the result would be the same.
Click to expand...
No = X
Study = Y
Fail = Z
X * Y = Z
Y = X * Z
These equations are almost never true, let alone for any value of X.
These are all of the possible solutions:
X^2 != 1 AND Y = 0 AND Z = 0
X = 1 AND Y = Z
X = -1 AND Y = -Z
 
Wow! With all respect, what ARE you trying to prove? And those arguing whether you can simpify the equation to arrive at the conclusion proposed and what not. What the… You can’t sum one thing and it’s opposite, they are incompatible states of existence. Either you study or you don’t. Either you are or you aren’t. (Unless you are a cat in box…) Period. End of argument. I won’t even mention the causality assumed between study and certainty of success… Yeah, maybe, maybe not. But wasting time on this kind of stuff won’t improve your chances of passing. And that’s a certainty.
 
1. “You can’t sum one thing and its opposite” is incorrect.
2. This is a silly thought exercise.
3. Most of us passed Level I, so it’s irrelevant whether this helps us pass.
 
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.
 
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 :)
 
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.
 
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