1 != 0.999...Quote:
Originally Posted by random25
Why? 1 is something that exists in nature, but there's nothing truly infinte out there. ;)
Fredi
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1 != 0.999...Quote:
Originally Posted by random25
Why? 1 is something that exists in nature, but there's nothing truly infinte out there. ;)
Fredi
Actually 0.999... is a number on the real line, it's another representation of 1. Go back to the first post for a couple of proofs.Quote:
Originally Posted by random25
Anyway, if 0.000... 1 was a real number, then it would be representable by 1/(10^p) where p is some positive integer. The only thing that might come close to making sense would be if p is infinity, but that would make 10^p equal to infinite and 1/(10^p) undefined.
The reason it does not have a representable form is because you're saying that an unending series of numbers has an end. It's a contradiction of itself.
What are your problems with the proofs at the beginning of the thread anyway?
he doesnt like to be wrong.
How about the universe?Quote:
Originally Posted by Subway
:pQuote:
Originally Posted by silverx2
None of your flawed mathematics prove 1 = 0.999...Quote:
Originally Posted by yasunobu13
You are only showing that our system of mathematics can not properly handle infinitely small numbers.
If you destination was 1 light year away, and you travel 0.999... light years you would be an infinitely small distance from where you are supposed to be.
Nope, you'd be there because 0.999... = 1Quote:
Originally Posted by random25
What are your problems with the proofs at the beginning of the thread anyway?
If the universe started with a big bang, than there must be an event horizon somewhere as we have the limiting speed of light. This means the volume is finite and the particles, energy, whatever in it can only be finite as well as there's a limit to how small things can be (quantum mechanics). I know there are other theories, but this one is currently the most popular, so I stick to it for the this discussion.Quote:
Originally Posted by random25
Fredi
That depends on what the definition of "is" is.
1 == 1 and 0.9999999... is and will ALWAYS be 0.9999999! Nothing more or less.
magnus your wrong.
0.1 divided by an infinitely large number would equal the difference between 1 and 0.999...
1 - 0.999... = 0.1/100...
If that is not true according to our system of math then our system of math is flawed. :p
Geeez,
I must be really bored to be going on about this...
Or more precisely:
1 - 0.999... = x/100...
Where x>0
Fredi
No.Quote:
Originally Posted by silverx2
(I wrote wrong. 0.9999999... is and will ALWAYS be 0.9999999...! Nothing more or less.)
Sorry guys, but if you look at the Wiki article I posted, you will see that 1 is in fact exactly equal to 0.999...
As someone said, what is the difference between the two? If you subtract 0.999... from 1 you should end up with a number n. If you use limits then you will see that the number n approaches 0 as the number of nines increase:
1-0.9 = 0.1 = 1/10
1-0.99 = 0.01 = 1/100
1-0.999 = 0.001 = 1/1000
...
1-0.9.... = 0.00... 1/inf = 0
Most of you (Subway) have tried to disprove the first proof, but not the second.
Someone else also pointed out that 1.999... = 2, and this is also true. Argue all you want, but this is the way mathematics is :)
I blame the matrix. ;)
Fredi
Ha! Now that I have proven you wrong, can you go back to fixing the problem I pm'ed you about? :)
I've already done all I can do. Now we can only wait, hope and pray. ;)
Fredi
PS: Did you know that your Firefox extension update file is the most accesed file on my server? About 10'000 times each day.
Oh.. well if the wiki says so, then i must be wrong. :doughnut:Quote:
Originally Posted by ihoss.com
If you use limits then you are no longer dealing with 0.999 carried out to infinity,Quote:
Originally Posted by ihoss.com
You are dealing with 0.999 carried out to some finite number of places then rounded up.
I end my contribution to this thread with: Between 1 and 0.999... is the smallest possible gap and a gap is never 0 :)
Fredi
There is a number between 0.999... and 1, but its not real, just like (-1)^(1/2) and 1/0. If we are dealing with the real number line, then the number between 0.999... and 1 does not exist, and if there is no number between them, they must be the same (on the real number line).
The math is not flawed, only your understanding of it.Quote:
Originally Posted by random25
If you were right and 1 - 0.999... = 0.1 / 100... then (as I said before), you can represent that number as 1 / 10^p where p is some positive integer, but that number would have to be infinity which makes the number undefined.
I don't know when you'll actually answer my question, but I'll keep asking you.
What are your problems with the proofs at the beginning of the thread anyway?
Nope, the gap is exactly 0.Quote:
Originally Posted by Subway
I don't know why some of you keep pretending this isn't correct, or that there is some indescribable distance between 0.999... and 1, or even saying that math is flawed without even saying why or how. Numbers can have more than one representation while continuing to equal each other.