Just watched this TED-Ed talk by Dennis Wildfogel on “How big is infinity?”
Apparently, infinities are not all the same. The set of numbers containing all the whole numbers is infinite, but it appears that this infinity is less than the set of rational numbers, which is also infinite, but if you map out both sets, you’ll find that the set of rational numbers is much bigger than that for whole numbers. Similarly for irrational numbers over rational numbers.
The different scales of infinities available eventually became a famous problem called the continuum hypothesis, an unsolvable problem in mathematics. As in, it’s proven to be unsolvable, not that it is not solved now but might be solved later on.
Found all these interesting and intriguing. Wonder what these mathematicians do for a living last time..
Never Stop Learning! 