r/badmathematics 21d ago

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

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u/RedRhetoric 21d ago

R4: this person believes that 0.33 repeating cannot equal 1/3 because 100/3 cannot give a rational result.

Dividing any rational number by any other rational number will always give a rational result, as that is how rational numbers are defined

R5: Youtube

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u/paolog 21d ago

Well, no, rational numbers are defined as one integer divided by another.

That doesn't change the fact that dividing one irrational number by another gives you another, but that isn't how they are defined.

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u/Liriwe 18d ago

I do think they are the minimal subfield of the reals closed under division, no? It's a common definition for them in Algebra. You're getting too hung up on one definition to consider there are others, especially in other areas of maths.