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.
didn't Richard Prior become rich off of this in Superman II?
no Subway, an infinitly small gap is equal to 0. if it is not, then its not infinitly small, only very small.
flash thinks
trace(1 == 0.99999999999999999) //true
trace(1 == 0.9999999999999999) //false
Flash is discrete and therefore not a good measure of reality in these situations.
I just can't agree on this one. An infinitly small gap can't be 0 or it would'nt be a gap anymore. An infinitly small gap is still a gap, infinitly small, but still a gap. You can add as many 9's as you want, it never completely reaches 1, yeah, even an infinte number of them, it's still less than 1.Quote:
Originally Posted by ihoss.com
It's the same with natural numbers. You can add 1 to any number, for an infinite time and you will never reach a limit. The same with 0.9999... you can add a new 9 as many times as you want, you never reach 1.
Fredi
I have to jump in here but, I think that 0.9999.... does = 1.
1/3 = 0.33333....
2/3 = 0.666666.....
3/3 = 0.999999..... or 1?
Any number divided by itself is = to 1 but....
0.33333...+0.33333.....=0.666666....
and
0.33333...+0.66666=0.99999....
and
1/3 = 0.33333
Believe me, this has already been discussed and it's been decided that 0.9999...=1 or the definition is: if two numbers are so close that you can't fit any more numbers than those numbers are equal. Sure 0.99999.... and 1 are two different numbers but by tweaking our math system they can be equal. Sure it's funky but until we get a better system that is able to deal with infinity then this is the best we have.
So if 1.0 == 0.999~ then 10000.0 == 9999.999~ ?
I think the winning argument here is "you can add a new 9 as many times as you want, you never reach 1."
and also this is pretty fool proof:
1 is equal to 1
2 is equal to 2
3 is equal to 3
0.999~ is equal to 0.999~
Can we stop this thread now? 4 pages is 4 pages too many for such a subject.
Math is clearly flawed!Quote:
Originally Posted by swak
Let's say you're limited to natural numbers (1 2 3 4 ...). So between 9 and 10, you can't fit another number! Does this mean that 9 and 10 are equal? No, of course not! This clearly proves that there's still a gap, even if you can't fit another number between! This means that the gap between 0.999... and 1 is a real gap and so both numbers can't be the same. If you make them the same, you destroy any logic that's left in math.
Fredi
Subway, as I said, the numbers are equal in the real world. as you said, there are no numbers between 4 and 5, but thats when you talk about natural numbers. The number between 0.999... and 1 is not defiend as a real number, just as 1/0 isn't. Its not imaginary either, is something else entirerly.
http://www.google.com/search?q=0.999...ient=firefox-a
One little google search and I didn't look into the pages but I think that most if not all say that it does. Also, I'm sure that by any calculator you use, 3/3 is = 1 so if 1/3 is equal to 0.3333.... then how does that work?
In effect you could also in a round about way say that 1=0 (I was kind of thinking of this) but our current understanding of infinity is messed up so our math is going to be messed up as well as long as it deals with infinity. Why do you think that it's taken so long for scientists to simulate a black hole? Sure 0.99999.... doesn't = 1 but than again it does. This argument will last as long as it will take to create new math that does in effect work out this problem accurately instead of using the assumptions that we use in today's society. It's likely that a majority of us will not be running into this problem and have to solve it. I very much doubt that any of us will have to worry about infinity unless it's apart of your job. Like I said earlier, this has already been argued and decided although I think that it really depends on what field you are in.Quote:
Originally Posted by http://karpus.wordpress.com/2006/06/21/apparently-0999-1/
No.Quote:
Originally Posted by ihoss.com
1-0.9.... = 0.00... 1/inf ~ 0
Yeah I would agree on this one. Iam thinking of this on a physical perspective. There is always a little gap between everything. What we say 'Solid' is always gonna be formed by loose particles, which then again are loose in themselves and so on, and that looseness is nothing but just another gap inbetween them....n. And please don't tell me that this going off from maths to physics and Iam not sticking on to maths, because (a) Iam not the one discussing about assumptions, (b) I just felt like saying this.... :zzz:Quote:
Originally Posted by Subway
Edit: Another thing...........arrrghh I can't control myself, but I do believe that not everything in maths can proved right or wrong (a=b and b=c hence a =c is not always right in real world), that's why the word 'Assumption' is of a very high importance. Happy self mind *******
If there is no gap between 1 and 0.999...,
and if 0.000...1 is not real,
this code should eventually get to 0.
Run this in flash and let me know when it gets to 0.
A number cant be 1 and not quite 1 at the same time.Code:for (var i = 1; i>0; i*10) {
gap = 1/i;
if (gap=0) {
trace("999... = 1");
}
}
A infinitely small gap cant be a gap and not a gap at the same time.
Just because we don't know how do infinite math doesn't mean that rounding off an infinite number at some point is really correct.
By definition of the word "infinite", 0.999... will continue on forever not being 1.
But our system of math cant deal with an infinite number, so you have to round it up to 1 in order for it to be usable.
Or maybe i am wrong, care to show me an example of a way our math system can work with infinite numbers?
Ok, listen up guys. This is the way it is, sorry. If you have an infinetly small space then there is no space between it, definetly not 0.00...1 wide, because that would mean that its not infinitly small.
Either accept it, or try to understand it. if you wont, you are wrong :)
I see it differently: Make a math system where infinite can never occur! No more division by zero bugs!
Fredi
Ok, listen up guys. This is the way it is, sorry. If you have an infinitively small space then it is a space no matter how small.
Either accept it, or try to understand it. if you wont, you are wrong :)
Believe what you want, but you can not prove it other than trying to using a flawed system of mathematics.
Or did you manage to get the code i posted to get to 0?
:thumbsup:Quote:
Originally Posted by Subway
1) a computer will never show this to you as a computers are discrete. This means they have a limited number of possible values that can be represented.Quote:
Originally Posted by random25
What you are doing in the above code is similar to trying to find the machine epsilon of your processor. That is the smallest possible floating point value that your machine can represent. A better way to compute this value is this:
Theoretically, that code should loop forever since dividing a positive number by another positive number will always be greater than 0, but due to the inherit limitations of discrete computation, the code will end rather quickly. I just did this in Ruby and got an output of about 4.94 * 10^(-324)Code:e = 1.0;
old_e = 1.0;
while(e > 0.0)
{
old_e = e;
e = e / 2.0;
}
trace(old_e);
trace(e);
2) your code has a bug in it, in the if statement you assign gap the value zero which will evaluate to a false statement no matter what the computed value of gap was initially.
3) depending on whether or not flash is computing with floating point numbers or integers, your code may or may not end. If i is a floating point number, it will eventually assume the machine's special infinity representation which will always be considered greater than 0. If it uses integers, then i will assume the special integer infinity or will overflow. Only in the case of an integer overflow will the program halt.
I don't know what flash uses for computations like that, but those are all of your options. Note that none of the options come anywhere near proving or disproving what we are talking about. For that you'll need to use mathematical proofs. And really, everyone, don't bring in computers or calculators into this discussion, they handle small floating point values bad enough.
No one is really arguing this.[/quote]Quote:
A number cant be 1 and not quite 1 at the same time.
A infinitely small gap cant be a gap and not a gap at the same time.
No one is rounding off except you. All this non-sense about "infinitely small" that you repeatedly failed to describe using proper mathematics.Quote:
Just because we don't know how do infinite math doesn't mean that rounding off an infinite number at some point is really correct.
You speak as though it takes time for a number to assume it's value. Yes, 0.999... has 9's that repeat "forever." "Forever" being a measure of time means that you will never be able to write the complete number out, but that doesn't mean that the number can't exist. Keep track of how you write, this isn't a problem that deals with space or time.Quote:
By definition of the word "infinite", 0.999... will continue on forever not being 1.
1) yes, math works with infinite numbersQuote:
But our system of math cant deal with an infinite number, so you have to round it up to 1 in order for it to be usable.
2) this issue has nothing to do with infinite numbers, you keep bringing it up for some reason that is beyond me.
3) none of the proofs that show 1 = 0.999... involve rounding.
I have no idea what you're expecting here. Some of the basic ideas areQuote:
Or maybe i am wrong, care to show me an example of a way our math system can work with infinite numbers?
infinity + infinity = infinity
infinity + (any real number) = infinity
1 / infinity = undefined
infinity / 2 = infinity
comparing the size of sets that have an infinite number of many members
Summing infinite series - They talk about how 0.999... = 1 near the end as well.
And I'll ask again: What are your problems with the proofs at the beginning of the thread anyway?
your code had bugs:Quote:
Originally Posted by random25
This is the output:Code:for (var i = 1; i>0; i*=10) {
gap = 1/i;
if (gap==0) {
trace("999... = 1");
break;
}else{
trace(i);
}
}
:DCode:9.99999999999999e+300
9.99999999999999e+301
9.99999999999999e+302
9.99999999999999e+303
9.99999999999999e+304
9.99999999999999e+305
9.99999999999999e+306
9.99999999999999e+307
999... = 1