0.9 repeating = 1

@buzzywasps said in #27:
> that doesn't mean it's equal to 1
It does because if x is a real number that is neither smaller nor larger than 1, then x has to be equal to 1.

@LD123 said in #13:
> no matter how long you repeat the 9's, it will be just a teeny tiny bit smaller than 1

This is a misconception coming from you not understanding what "infinity" means. "No matter how FINITELY long" you repeat the 9's you are right - but if you repeat them INFINITELY long you are wrong. Think bout this:

We start with 1 "9": "0.9" - we have indeed a difference between 1 and 0.9 of 0.1.
Continue with 2 "9"s: "0.99" - we have a difference of 0.01.
Next is 3 "9"s: "0.999" - the difference is 0.001

And so on. If you have infinitely many 9's you have a difference of "0.<infintely many 0's>1" - but the "1" will never come into place, because *infinitely many* zeroes are never exhausted - whenever you want to put the 1 there, there will still be infinitely many zeroes going first. And however many zeroes you put in, there will still be infinitely many to put there *before* the 1. Infinity minus any number is still infinity.

To say it in a form an mathematician won't cringe at: if a difference can be smaller than any finite value you can think of - then this difference is infinitely small - and hence zero.

Just to settle the debate, I lay out a challenge to anyone on Lichess. If you can prove that there is a number in between 0.999... and 1, everyone saying that they are not equal will admit that you are right and, just because I am laying this challenge, I will close my lichess account and never play chess or post in any forum anywhere ever again.

prove to me its equal to 1

@LD123 I did it in #3, then in #7, then again in #26, and finally, in #30.

im not convinced.

@LD123 Alright, in the grand-scheme of things, you not being convinced is completely irrelevant. The reality is, I have provided 8 methods that clearly show that 0.999... =1 and anyone who has a basic understanding of math would be able to understand at least 6 of them (the 2 involving sums are a bit more complicated so I will let it pass if you don't understand them). So really, you not being convinced and not being able to provide an explanation for why you are not convinced goes on to show that you can't understand basic math.

I went over several of your math statements and questions and believe they will help you pass a couple of online assessments. I use brighterly.com/homeschool-math/ for myself because I work as a math instructor and need to refresh my memory before each lecture.

If you take 1-0.99... WHat do you get
In math theory, two numbers are numbers if there is a number IN BETWEEN them. It must have a value if one substract another
So what is in between 1 and 0.99...?
Nothing. Because 1.1 and 1 are numbers and 0.99... don't have a last number.
So 0.99...=1