sadly this proof is invalid. I offer my counter argument. (no study + study) = (no fail + fail) can be written as (no study + yes study) = (no fail + yes fail) factoring study and fail gives (no + yes)*study = (no + yes)*fail, or 0*study=0*fail. here, you divided both sides (cancelled) by 0 to obtain study = fail. Since one cannot divide by 0, the proof is null and void. but how i wish it were true. then i could give up studying math altogether... : (
(No Study) and (no fail) in this case need to be treated as one variable since 'no' looks the same but is different. You can't just split two variables in half.
Study=pass no study=fail study*no study=pass*fail 1*0=1*0 whereas study is 1 meaning that it exists, no study is nothing. Pass is a passed test where fail is not a passed test. Therefore to study and not study is technically "schrodinger's cat", where two variables exist at the same time until you 'look in the box'.
That is assuming yes = 1 and no =-1, if im not mistaken in binary, yes is basically 1 and no is basically 0, thus (yes +no)study=(yes+no)fail 1(study)=1(fail) study=fail
But its the "No Fail" that is the problem. Its assumed that "No Fail" equals "No" x "Fail", but that dosn't make sense. What is "No" times "Fail"? "No Fail" is a single statement, like "NoFail"... but then there would be no joke. And I like jokes.
Instead of working with the words No, Study, and Fail, let's replace them with x, y, and z, so that we are not confused with the symantic meaning of those words. After we do the math, we will return to the symantics. So, we have:
1) x y = z 2) y = x z
From 1), y = z/x, and from 2), y = xz, therefore: z/x = xz 1/x = x x^2 = 1 x = 1 or -1.
Now let's return to the symantics to figure out of x is 1 or -1.
If x is 1, then No Fail = Fail. That makes the conclusion of this proof true, but meaningless.
If x is -1, (which makes good symantic sense), then (No + 1) = 0, so you are dividing by zero.
