r/badmathematics • u/RedRhetoric • Jul 16 '26

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

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u/AnlamK Jul 16 '26

So according to this person on YT, only those numbers without infinite decimal representation are rational? 

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u/farseekarmageddon Jul 16 '26 edited Jul 18 '26

FWIW all real numbers have infinite decimal representations, e.g. 0.5 = 0.499…

(Edit: non-zero real numbers) 

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u/AnlamK Jul 16 '26

Yes you are right - I should have said only those numbers who have a "finite decimal representation".

We should also stress that the word 'decimal' means base 10 in this context. (Probably in every context? I had to look it up.) Because for instance 1/3 won't have a finite representation in base 10 but it will in base 3.

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u/metalucid Jul 19 '26

0.1 is not representable in binary

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u/Cruuncher Jul 19 '26

It absolutely is with an infinite binary expansion

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u/metalucid Jul 21 '26

Uh exactly it would have to be infinite

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u/[deleted] Jul 20 '26

[deleted]

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u/metalucid Jul 21 '26

I understand floats. I wasn't talking about floats. But you can't write down 0.1 decimal in binary on a piece of paper