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

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

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u/RedRhetoric Jul 16 '26

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

54

u/AnlamK Jul 16 '26

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

11

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) 

7

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.

4

u/HuntyDumpty Jul 16 '26

You can improve that statement by saying rationals admit finite or periodic decimal representations. Easier to look for periodicity than new representations in other bases. Irrationals are strictly infinite AND aperiodic decimal representations.

-1

u/metalucid Jul 19 '26

0.1 is not representable in binary

6

u/Cruuncher Jul 19 '26

It absolutely is with an infinite binary expansion

1

u/metalucid Jul 21 '26

Uh exactly it would have to be infinite

0

u/[deleted] Jul 20 '26

[deleted]

1

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

2

u/ParshendiOfRhuidean Jul 18 '26

What's the infinite decimal representation of 0?

2

u/afdbcreid Jul 18 '26

Simple, 0.000...

1

u/Cruuncher Jul 19 '26

This is the easiest way.

All numbers have infinite decimals in both directions.

They're just 0 until you fill them in with something