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> We cannot imagine infinity Now try imagining that some infinities are bigger than others: https://en.wikipedia.org/wiki/Aleph_number https://en.wikipedia.org
by laichzeit0 6y ago
> We cannot imagine infinity
Now try imagining that some infinities are bigger than others: https://en.wikipedia.org/wiki/Aleph_number https://en.wikipedia.org/wiki/Aleph_number
- LunaSea 6y agoThis is one of my pet peeves in maths. Although I do understand the concepts presented, the notion of "greater" makes no sense when applied to something without boundaries. Yet it's used all the time.
- petters 6y agoPersonally, I think it makes perfect sense. Take two sets A and B. If we can assign every element in A to a different one in B, we say that |A|≤|B|. Makes perfect sense for normal, finite sets, right? As it happens, this definition extends to infinite sets as well.
- erodommoc 6y agoRight, but many things make sense for finite sets that don't make sense for infinite sets. Just because you can extend that definition doesn't mean that it's "true" for infinite sets.
- laichzeit0 6y agoThings quickly fall apart if you rely on your intuition. Let's imagine all the odd numbers: 1, 3, 5, etc. Now imagine all the even numbers: 2, 4, 6, etc. Can we agree that there is an "infinite" amount of numbers in each of those groups? Now imagine all the odd numbers and even numbers together. That's also infinite right? Would you say there are more "all numbers" than just "all odd numbers", or would you say that there are an equal number of them? (hint: the answer is equal).
- erodommoc 6y agoWell, the answer is equal because of how you define equality of infinite sets (one-to-one and onto). It's a very useful definition, but it's hardly the only possible definition.