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You could make the same argument against the real numbers. Almost all of them cannot even be written down or described, so it's hard to say how they map to the
by defen 11y ago
You could make the same argument against the real numbers. Almost all of them cannot even be written down or described, so it's hard to say how they map to the real-world. But the concept of real numbers is extremely useful for a large number of mathematical proofs.
- reagency 11y agoWhich proofs depend on an infinitely discontinuous subset, though?
- ColinWright 11y agoIt's not that we rely on such things, but that these things are unavoidable consequences of choices we make that seem to be perfectly reasonable, and result in useful math. Phrasing in the other way: As we develop math that we find useful and powerful, we find that we have to make choices. Those choices have consequences, and sometimes as we explore the consequences we find that really strange things happen. We can go back and make different choices, but in practice we tend to find that no matter what choices we make there are odd and hairy things that result.
- ebola1717 11y agoThe natural way to encode an infinite binary tree into the real numbers is as the Cantor set, an uncountable totally disconnected set.