The most startling thing I've learned in this summer is that numbers such as .9999....(where the nine's go on forever) and 1 are equal. (Perhaps this isn't some startling and bizarre fact that most people don't know. Maybe I just slept that day in elementary school, but humor me here.)

Proof:

We know for any two values of x and y such that x/3 = y/3 that it must be that x=y.

Suppose x = .9999.... and y = 1.

Of course, .9999...../3 = .3333.....

And of course, 1/3 = .3333.....

So obviously, .9999/3 = 1/3 and, thus, .9999.... and 1 are equal.

Again, maybe I missed this in elementary school, but that seems fucked to me.