Are you into mathematics? Do you have any cake?

[Whateverist]

What's so "trololololol" about my question?

According to you guys it's absolutely impossible to divide a cake with no one but perfectly possible to add absolutely nothing to a cake.
You can't just "add" nothing to a cake, that would defeat the purpose of the addition operation in the first place, no addition took place there. So why is it okay to add nothing to a cake but not okay to divide a cake among no one? Seems like a perfectly reasonable question to me.

As Alex put it, division asks a more involved question than addition; it isn't just "what do you get?"  Division really asks: if you give an equal portion of an x amount to each of y, how much does each y get?  Implicit in the question is the idea that you hand out all of the starting amount, x.  If upon completing the division there is anything remaining, you simply didn't do it right and we can't call that division.  When you divide by 1 you aren't left with the entire cake, it was handed out to just one person.  If it was retained it was never divided up.

A good way to think of division is as the inverse of multiplication.  Where multiplication asks for repeated addition (eg, what is the sum of 4 threes), division asks if the sum of 4 of something is 12, what is that something -or- what would you need 4 of to total 12?  

So for the cake problem where you have 4 to serve you might ask: how much of the cake should each receive in order to use it up while giving each an equal share?  Answer: Each should receive a fourth of the cake.  But to divide it equally among 0 people, there isn't any amount which would use up the entire cake.  Since there is no way to accomplish the giving out an equal amount to zero people in such a way as to hand out all of the cake, the problem has no solution and really the question makes no sense.  The operation is being employed in a way that betrays a misunderstanding of its purpose and proper application.