I read logicalee's comment as a reference to the way most (all?) branches of mathematics may be built using sets and their axioms. Set theory boils down to "in the set" and "not in the set", ie. black and white.
Quite interestingly, the axioms mathematics is build upon do not let you decide every question that you might come up with. As such in mathematics not everything is black or white. For example, the continuum hypothesis is independent of the most commonly used axiom system ZFC. To explain what that means imagine ZFC would be describing an apple. Out of the definition of "apple" you can get theorems that tell you "if you start on any point of the apple and dig down in a straight line, at some future point in time you will reach the 'other side' of the apple" or some statements you can disprove "if you walk on the surface of the apple in a straight you will never come back to point where you started". What you will not get is the colour of the apple. Everything you know about the apple is consistent with it being green. But all that is also consistent with it being red. The colour of the apple is independent of everything that you are interested in in an apple. Therefore there is no reasonable answer to the question "which colour does the apple have", except maybe: It should not matter. The same is true of the continuum hypothesis. I remember reading that if you need the CH to prove something, then you should definitely reconsider the statement you are trying to prove :).
> I remember reading that if you need the CH to prove something, then you should definitely reconsider the statement you are trying to prove
This is not entirely true. There are many proofs that begin by assuming CH. There are also two ways of interpreting "need CH to prove". One way is that the thing you are trying to prove is equivalent to CH, which is an interesting/useful result. Another way to interpret it is that you can not come up with another way of proving it. In the latter case, the CH based proof justifies that your proposition is not inconsistent, and may even lead you (or others) to proof that it is true regardless of CH. If I recall correctly some statements have been proved by proving the statement when CH is true, and also when CH is false.
Ah but the real story is that like sophisticated math systems, in relation to any fixed axiomization, set theory involves provably, provably false and unprovable/independent statements. And in relation to any fixed model, set theory involves true and provable, true but unprovable, false but un-disprovable and false and disprovable.
And when you're math as a human endeavor, you can also add "provable but not yet proven" and "proven independent"
So, learn some stuff, see how far from black and white higher math can be.