Recently I've been thinking a fair bit about the concept of infinity. Mainly because of what I'm being taught on one of my courses, but the more I think about it, the closer my head comes to exploding.
I always just assumed infinity was, well, infinite. Something that never ends, which is a bit of a mind fuck in its own right if you stop for a few minutes and just think about it. Things got even more confusing when I was told that there isn't just one infinity, but several. Some infinities are larger than others. In fact, some infinities make other infinities seem tiny in comparison.
Think about numbers. You know that natural numbers (0, 1, 2, 3...) are infinite, but then if you stop and think about the rational numbers (0.0001, 0.0002, 0.0003...) you realise there's an infinite amount of them between each pair of natural numbers. Thus, the set of rational numbers is infinitely times larger than the set of natural numbers, which itself is infinite, right?
Anyway, I just find this interesting in a slightly nerdy way. I thought I'd try and get you guys to let your brains ponder for a minute or two.
- Has your head exploded yet?
- Does it makes sense to you that some infinities are larger than other infinities?
- What other naturally occurring things make your head come close to exploding when you think about them?
- Did I successfully make you stop and think about this?
Also, discuss infinity and stuff.