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Yeah, that's obviously just an ordering of the rationals.
by Retra 9y ago
Yeah, that's obviously just an ordering of the rationals.
- danbruc 9y agoI don't think it's that obvious, actually I think it's not actually an ordering of the rationals. If this were an ordering of the rationals, then it better included rationals with an infinite number of non-zero decimal digits, for example one third. But if this would include one third, then I am unable to see why it wouldn't also include square root two. Why would this be able to include repeating decimal expansions but not non-repeating ones?
- Retra 9y agoYou're right, I misread what you wrote. You're actually only covering a small portion of the rationals. Either way, to order the reals, you have to include the non-computable ones, which cannot be written down in any systematic way. This also means that ordering and equality relations cannot be systematically defined either.