3 ms·
You have described how the set of computable numbers are countable. But you have then posited "the set of the reals is uncountable" without any further explana
by frutiger 7y ago
You have described how the set of computable numbers are countable. But you have then posited "the set of the reals is uncountable" without any further explanation as to how that is the case. Your explanation helps one understand why computable numbers are countable (and that is for sure a useful insight), but says nothing about uncountable sets.
I still feel the diagonal argument is the clearest intuition for defining an uncountable set.
- mFixman 7y agoI was taught that real numbers were countable before learning what computables numbers where. "There's a set of countable numbers that includes every real number you know and doesn't include handwavy concepts" was news to me. Personally, I never found the diagonal argument intuitive. The proof with the nested open intervals in a sequence was easier for me to understand, but that's probably because I have more of a background in CS.