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Talk:Countable infinity is uncountable infinity
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This argument doesn't work because it only proves that terminating decimals are countable (which they are). Most real numbers have decimal expansions that never terminate (and never reach a repeating loop), but your argument isn't counting those. --ais523 21:08, 23 May 2025 (UTC)
- you bring up a convincing point before you realize that a number can be however long. even infinitely long. so for example, pi, could be ....356295141. like 10-adic numbers. 21:27, 23 May 2025 (UTC)
- But if you include infinitely long numbers that don't repeat, then you have uncountably many. The 10-adic numbers are only countable because they always end up repeating eventually. --ais523 21:30, 23 May 2025 (UTC)
- oh. ok, thank you for telling me this! 23:20, 23 May 2025 (UTC)