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if you put 1 out then there is no reason to believe it is uncountable because you can sort the list such that the diagonal is all 0s (if you know an argument th
by raoof 4y ago
if you put 1 out then there is no reason to believe it is uncountable because you can sort the list such that the diagonal is all 0s (if you know an argument that shows [0,1) is uncountable I'd be happy to know)
- Koshkin 4y agoWell, if you remove one element from an uncountable set, then...
- raoof 4y agoyou can't prove something just by assuming it that would be trivial, if we can build or convince ourselves how to build a wormhole or a time machine then we can believe in Real numbers
- d_tr 4y agoWhat Koshkin says is correct and has already been proven by others. You want to get a book that covers sets, maps and cardinal numbers, and read it carefully if you are interested in this sort of stuff.
- raoof 4y agoI can see that you can symbolically talk about the power set of (0,1) and say it's cardinality is bigger than the set itself (although I haven't studied sets and cardinalities deeply enough) but I can't see what Real numbers offers against the computable Universe hypothesis
- d_tr 4y agoIt is a superset of (0,1), which is uncountable because it is an open interval. All open intervals except the empty one are uncountable. What kind of proof would you like? There is also no such thing as an uncountable list. Lists can be indexed by integers, which makes them all countable.
- raoof 4y agothe proofs that I've read shows that the list of infinite binary strings between [0,1] are uncountable because the invert of the diagonal of the list is not on the list, do you know any proof that does not refer to the invert of the diagonal?