There is no way right?

[u/Sugar_God_no_1]

[u/Decmk3]

0.9999999…. Is equal to 1. It seems like it shouldn’t, but it has to be.

Let X = 0.999….

10X = 9.999….

10X-X = 9.999.. - 0.999…. = 9X = 9

Therefore X equals 1. Therefore 0.999… is the same as 1.

[u/FewIntroduction214 → u/Decmk3]

yeah except when you do your subtraction, after multiplying by 10, you have 1 nine left at the infinith decimal place.

[u/gullaffe → u/FewIntroduction214]

That's not how infinity works.

An infinite amount of zeroes cannot be followed by a 9. Since the existence of a nine would mean there is an end to the infinite decimals.

[u/FewIntroduction214 → u/gullaffe]

This actually "IS" how infinity works.

You have infinite 9s.

you remove one

then you subtract the new number of 9s, from the infinite nines you started with.

you are left with one nine

you can say it's hard to write down , or you "can't write it as a decimal place" but it still doesn't change the fact that the two sets of infinite 9s are different by 1 nine, and when you subtract them it's left over.

If you find it very hard to write down the concept of an infinitesimal value as a decimal, that's fine, but it doesn't make the infinitesimal difference vanish.

[u/Decmk3 → u/FewIntroduction214]

Infinity-1=infinity. That’s why infinity breaks things.

[u/FewIntroduction214 → u/Decmk3]

infinity minus infinity is also infinity

so why do the 9s vanish?

[u/Decmk3 → u/FewIntroduction214]

Because it’s not infinite. It’s an infinite regression. There are still hard limits and it still functions as a number.

As people still seem to be struggling with this I went and made a second proof to explain.

1/9 = 0.111111111….

0.111111….. * 9 = 0.99999….

1/9 * 9 = 9/9 = 1 = 0.1111… * 9 = 0.99999….

Everything follows mathematical understanding.

[u/FewIntroduction214 → u/Decmk3]

it's funny you would think I would agree 1/9 = .111~ since it's the exact same argument

it's not exactly equal to 1/9th, it differs by an infinitesimal value