[Mauzen]

So,
fail usually is a zero as it describes the absence of success or any valueable effect.

Now, as study isnt a general term, but rather describes a series of all different kinds of studying, lets name a single element of that series as study(x), where x Є N is indexing the elements. Assuming that study represents the intellectual gain as a number, study(x) Є Z might be positive or negative for all indexes.

now as study isnt a single number, but a series, you cant compare it with fail, which is a single number.
Following the standards the meaning of the equation would then rather be
Σ (x Є N) (study(x)) = fail = 0

Now using general knowledge, for any kind of study, there must be another study with the opposite effect, e.g. one study teaches you something, another one teaches the first one was wrong, so it has the inverted fain of the first study. Meaning
(FOR ALL) x Є N: Ǝ y Є N: study(x) = -study(y)

Using full induction you can now always find a pair of elements in study that nullify each other, proving that
Σ (x Є N) (study(x)) = 0 = fail
so
study=fail