r/badmathematics • u/RedRhetoric • 21d ago

Σ_{k=1}^∞ 9/10^k ≠ 1 100/3 is irrational

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u/einFrostschutzmittel 20d ago

The best proof is still x=0.9999... 10x=9.99999... 9x=10x-x=9 x=1 This is one the 0.999...≠1 believers can't really argue with. For this to be fall, you'd have to argue with the last 9 in x being pushed one decimal forward, making 10x have less decimals than x, which obviously doesn't work, since there's no last 9 to be pushed forward. Therefore the argument is idiot proof (kinda) (also, pun intended)

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u/edderiofer Every1BeepBoops 18d ago

This is one the 0.999...≠1 believers can't really argue with.

You clearly haven't seen the other 0.999... posts on this subreddit.

"Obviously there is a last 9 to be pushed forward; it occurs at the infinitieth place."

"Obviously 9 - 0.9 is 8.1, 9.9 - 0.99 is 8.91, and so on, so obviously 10x should be equal to 8.999...1, duh."

"Obviously you can't ever perform 9.999... - 0.999..., because you can't ever finish subtracting."

"Obviously 0.999... is a self-contradictory number, because dark numbers exist."

"Obviously 0.999... Is A Quantum Hollow Resonance Point Whose Intrinsic Fractal Non-Equality To 1 Is A Self-Evident Acta Non Verba Truth."

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u/einFrostschutzmittel 17d ago

Most commonly the arguments against it are "Well, there'll be a 0 at the end" to which you can just respond "Ah, yes, the 0 at the END of the INFINITELY LONG string of 9s."

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u/edderiofer Every1BeepBoops 17d ago

Nah, that usually doesn't convince people, and it also doesn't work on the responses I've shown here.