I was taught that real numbers were countable before learning what computables numbers where. "There's a set of countable numbers that includes every real numbe

I 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.