[00:02] random because formulas always give the same result, which is why computers don't have true random number generators. Instead, they usually run an algorithm on your current local time to generate numbers that appear random. So,
[00:16] if we can't pick randomly, how do we select anything in math? Well, the only way is to follow a rule of some sort. So, a rule could be always choose the smallest thing. For example, if we're looking at whole positive integers, the
[00:31] smallest is one. For prime numbers, it would be two. Easy. But, what about the real numbers? That's any number, positive, negative, whole, fraction, even irrational, like pi or the square root of two.
[00:44] Now, try to choose the smallest one. It's impossible. The real numbers stretch off to negative infinity. Even if we try to fix our rule by making it super specific, like choose the smallest number after one, we still get
[00:58] stuck. There's 1.01, then 1.0001, then 1.00000001, and so on. and so on. So, really, what number comes after one?
[01:13] If we can't begin to specify the order of the real numbers, next and previous, first and last, we're stuck. The ridiculous part is we know we have infinite options, but despite that, we can't figure out how to just pick one.
[01:27] The mission to resolve this began with one man in 1870. He took on the task of putting the real numbers in a definitive order, even if it killed him. And, it nearly did.