I know nothing about mathematics, but I did hear that 0.999... = 1. I was thinking about it for a moment, and I thought of something that I think may be a proof of it. I didn't find it among other common proofs of it, so is it just trivial, or a load of shit? Here it goes.



0.9999.. is infinitely close to 1, because there is no specific number that is a distance between them. 



Therefore (1-0.999...) is infinitely close to zero.



Therefore 1/(1 - 0.99..) is infinitely close to infinity.



Now a real number cannot be infinitely close to infinity, as any real number can have one higher than it. Therefore it is infinite. 



Therefore (1 - 0.99..)=0



Conclusion: 0.99... = 1

>>15378548 (OP)

0.999... is not a number. 0.999 is, and it is 0.001 away from 1.

brainrot retard

>>15378548 (OP)

>0.9999.. is infinitely close to 1, because there is no specific number that is a distance between them.

This is (more-or-less) all you need. If you can't find anything at all in between two numbers, they're the same number.

>>15378548 (OP)

>Now a real number cannot be infinitely close to infinity

Look at this pleb who never heard about Tooker's infinity hat construction.

I already did clarify that I knew nothing about proof-based mathematics

>>15378548 (OP)

Any number not divisible by 3 divided by another number that is divisible by 3 will create this problem because we use a base 10 number system. 1/3*3 is 1, not .999....

>numbers exist

just count with letters op

>>15378548 (OP)

>I know nothing about mathematics

And yet you btfo'd 90% of /sci/ without even trying. Godspeed op, mathlets will seethe ITT

>>15378548 (OP)

A lot of steps could be stated more clearly or more accurately, but this is more or less the gist of the standard proof. The idea that a number cannot be infinitely large is called the Archimedean property.

https://en.wikipedia.org/wiki/Archimedean_property



I should make a correction, though:

>Now a real number cannot be infinitely close to infinity, as any real number can have one higher than it.

This step doesn't follow. There would be no contradiction in doing 1/(1 - 0.99..) + 1. We have to specifically construct the real numbers in such a way that the Archimedean property holds.

Not sure what OP meant by specific, so I'm going to guess it means a number that can be named by a fraction/decimal rather than by just saying "(1 - 0.99..)". Having difficulty naming the number doesn't mean the number doesn't exist. A more careful version would note that any positive rational number must be greater than (1 - 0.99..), then proceeding with more or less the same subsequent steps OP did.

>Having difficulty naming the number doesn't mean the number doesn't exist.

Self-correction: For the case of the reals, it implies that the number doesn't exist, but you have to actually prove that every real number has a decimal representation instead of just assuming it. (Unless you take infinite decimals as your model of the reals, but that ends up being overcomplicated and not very satisfying.)

>>15378548 (OP)

>I did hear that 0.999... = 1

Where?

>proof

If you've never opened a math book I'd say you did very well.

>There are retards on this board that think 1/3 doesn't equal .3333333333333....

it's an infinite series retard

>>15378548 (OP)

A little off if this in a very serious class but very nice, I am sincerely impressed!
