You'd be amazed how much we use the floor function in number theory. After all, our main area of concern is the natural numbers, so whenever we step outside them and use other kinds of math (which is all the time), we need a way to translate our answer back to the integers. One simple example: counting digits of numbers. The first n-digit number is always 10n-1, so if we have an unknown number x and want to know how many digits it has, what we're "really" asking is which two powers of 10 it lies between. Thus 10n-1 <= x <= 10n n-1 <= log x <= n Thus n-1 is floor(log x), or n is ceil(log x), whichever you like. We've answered our strictly integral question by stepping outside the integers, then using the floor function to step back in. These are base-10 logs, by the way. Counting digits is the one context in pure math where we use them. More on reddit.com

“Mathematical operations” (i.e. arithmetic) are only a small part of math. A relation is simply a mapping of elements in one set to elements in another set, and that’s what the floor and ceiling functions do. More on reddit.com

double ceil(double a) { auto b = double((long long)a); if (a < 0 || b == a) { return b; } else { return b+1; } } EDIT: fixed negative number behavior and casted to larger to integral type per u/bad_investor13 More on reddit.com

de Morgan's laws but epic More on reddit.com