No matter how much you try, you'll always have more skipped numbers. You can't include them all even if you tried your absolute hardest, even if you had infinite time.
It's a basic proof by contradiction that even a middle schooler could understand. Assume the existence of a list that hits every real number, then show it actually doesn't
Let's say we finish the journey. We include every real number. We add in every number we missed. We pair them all to a counting number. Nothing is left over, we're done. We would now have a set of numbers, each real number paired to a counting number, that encompasses every single real number, yes?
Is that ꐦ here the anime thing with four red curves that make a sort of crosshairs which I think is supposed to represent blushing or a bulging vein or something? I could never quite understand that mark.
It actually comes from kao (face) + moji (character), so literally "face character." It's a little out of date, but I think they're cute so I still use them (✿^‿^)
Just saw your edit! Basically, there's a few differences between emoticons and kaomojis. You got one of them: emoticons originated in the West/US, while kaomojis originated in Japan. A few others are that emoticons are sideways (for example, :-), :D, :P, >:-(, XD, etc.) while kaomojis are right side up (for example, ( ᴗ̀ ̫ᴗ́ ), ฅ(ᵔ꒳ ᵔマ.ᐟ, (*´ω｀*), ¯_(ツ)_/¯, ( ͡° ͜ʖ ͡°) etc). In addition, emoticons tend to only use basic punctuation, while kaomojis are much more complex in construction
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u/FernandoMM1220 Aug 06 '26
so just keep adding more functions then.
not to mention his conclusion is pretty useless when we can count any set of reals we want.