Imagine that such a number 0.000...01 did exist.
There would be an infinite number of 0s, and therefore you never reach the one. The entire concept of a non-terminating decimal is that you cannot pick a digit and say "this is the last digit" because you will never get there. Every time you might reach the 1 at the end, there are still infinitely more 0s before you can reach it.
its really simple when you look at fractions
like 0.3˘ x 3 (dunno how to do right symbol)
What are people trying to prove here? Math, or what numbers represent and how they work?
Middle can be any digit that is infinitely far away from the extremities of the number, the argument stays the same.
Let's take a semi-line if you prefer. It has a defined start but stretches to infinity. if you place the origin of your referential on infinity, the origin of the line will be located at infinity, but it will still be there, it'll exist. Not in a finite distance, but it'll be there.
0.999... = 1 because we don't allow for infinitely small numbers in our math.
This does not prove anything.
Using infinity to prove something is on par with dividing by zero. As far as we know, a true zero or a true infinity does not exist in our universe, so ultimately we are going to make up its properties, so of course 0.999... = 1. That's what the made up properties of infinity tells us.
0.111... = 1/9
0.222... = 2/9
0.333... = 3/9
0.444... = 4/9
0.555... = 5/9
0.666... = 6/9
0.777... = 7/9
0.888... = 8/9
0.999... = 9/9 = 1 end of thread
I feel like this thread should have ended at the OP because there was a perfectly reasonable proof right there. But some people are like "Fuck that; I may be a high-school student who failed algebra 1 but I know better than all of the mathematicians in the world!"
ITT: People in thread do not understand concepts of higher mathematics such as, infinite series, induction and convergence.
Definitions for continuity are carefully chosen so that they rely only on finite numbers.
Isn't this just proving that our ways of thinking are broken rather than making sense?
If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses, it's 1 glass devided in 3. Saying it's 1/3 is fine, but saying it's 33, etc % is wrong. Just because we can't devide 1 into 3 efficiently doesn't mean it's content is 0,9. Assuming that this flaw makes it right to say 0,9 is actually also 1, is just as flawed or even worse.
Besides, 0,999 is infinitely far away from being 1. Just because infinity isn't a number doesn't mean it's not there. And even if it was a number, it can never become something between 0,999 and 1 unless you make up some new rules.
But yeah i am probably too dumb for this with my elementary level math.
Well, I don't mean picking a number just like that. I can't say how it looks like or write it, I can only say it's infinitely close to a number. but if that means the difference is 0, then it is the number itself. So doesn't it form an infinitesimal gap?
Never mind, it's a bad argument.
If you pour a glass of water into 3 glasses with exactly the same amount in the 3 glasses it's 1 glass divided in 3. So there is 1/3 in each. 1/3 = 0.3... Multiply it by 3 and you get 0.9... which is everything you had, which is 1.
1 = 3/3 = 1/3+1/3+1/3 = 0.3...+0.3...+0.3... = 0.3... x 3 = 0.9... These are all equal.
I only watched this to fap to the sound of her voice.
My math teacher did so many proofs on this... Can we all just agree .999(Repeating) = 1.
So what is the difference between 0.999... and 1?
My brother told me another way to think about it.
What is 1 minus 0.9...
The answer is 0.0...
That is a fancy way of saying zero. So if 1-0.9... is 0 they must be the same value.