this post was submitted on 27 Jun 2024

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submitted 6 months ago by [email protected] to c/[email protected]

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[–] [email protected] 93 points 6 months ago* (last edited 6 months ago) (44 children)

x=.9999...

10x=9.9999...

Subtract x from both sides

9x=9

x=1

There it is, folks.

[–] Shampiss 23 points 6 months ago (2 children)

Divide 1 by 3: 1÷3=0.3333...

Multiply the result by 3 reverting the operation: 0.3333... x 3 = 0.9999.... or just 1

0.9999... = 1

[+] [email protected] -9 points 6 months ago (2 children)

You're just rounding up an irrational number. You have a non terminating, non repeating number, that will go on forever, because it can never actually get up to its whole value.

[–] [email protected] 11 points 6 months ago (1 children)

1/3 is a rational number, because it can be depicted by a ratio of two integers. You clearly don't know what you're talking about, you're getting basic algebra level facts wrong. Maybe take a hint and read some real math instead of relying on your bad intuition.

[+] [email protected] -11 points 6 months ago (2 children)

1/3 is rational.

.3333....... is not. You can't treat fractions the same as our base 10 number system. They don't all have direct conversions. Hence, why you can have a perfect fraction of a third, but not a perfect 1/3 written out in base 10.

[–] [email protected] 14 points 6 months ago

0.333... exactly equals 1/3 in base 10. What you are saying is factually incorrect and literally nonsense. You learn this in high school level math classes. Link literally any source that supports your position.

[–] [email protected] 5 points 6 months ago (1 children)

.333... is rational.

at least we finally found your problem: you don't know what rational and irrational mean. the clue is in the name.

[–] Klear 1 points 6 months ago (1 children)

TBH the name is a bit misleading. Same for "real" numbers. And oh so much more so for "normal numbers".

[–] [email protected] 3 points 6 months ago (1 children)

not really. i get it because we use rational to mean logical, but that's not what it means here. yeah, real and normal are stupid names but rational numbers are numbers that can be represented as a ratio of two numbers. i think it's pretty good.

[–] Klear 1 points 6 months ago (1 children)

I know all of that, but it's still misleading. It's not a dumb name by any means, but it still causes confusion often (as evidenced by many comments here)

[–] [email protected] 3 points 6 months ago

fair enough, but i think the confusion for that commenter comes from a misunderstanding of the definition of the mathematical concept rather than the meaning of the English word. they just think irrational numbers are those that have infinite decimal digits, which is not the definition.

[–] [email protected] 5 points 6 months ago

non repeating

it's literally repeating

[+] [email protected] -20 points 6 months ago (2 children)

In this context, yes, because of the cancellation on the fractions when you recover.

1/3 x 3 = 1

I would say without the context, there is an infinitesimal difference. The approximation solution above essentially ignores the problem which is more of a functional flaw in base 10 than a real number theory issue

[–] Shampiss 23 points 6 months ago* (last edited 6 months ago) (1 children)

The context doesn't make a difference

In base 10 --> 1/3 is 0.333...

In base 12 --> 1/3 is 0.4

But they're both the same number.

Base 10 simply is not capable of displaying it in a concise format. We could say that this is a notation issue. No notation is perfect. Base 10 has some confusing implications

[–] [email protected] 9 points 6 months ago

This seems to be conflating 0.333...3 with 0.333... One is infinitesimally close to 1/3, the other is a decimal representation of 1/3. Indeed, if 1-0.999... resulted in anything other than 0, that would necessarily be a number with more significant digits than 0.999... which would mean that the ... failed to be an infinite repetition.

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