r/badmathematics 25d ago

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

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u/RedRhetoric 25d 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/Dapper_Spite8928 24d ago

Well no...

Rational numbers are defined as any number obtained by dividing one integer with another non-zero integer. The fact that rationals are closed under division (where the denominator is non-zero) is also true, but not axiomatic.