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Ok, in base 10 we have 10 different numbers before they are repeated. Look at this:
0.000000000... obviously is equal to zero
0.999999999999... must be at the other end of the extreme, which is 1.000000000...
0.000000000000... is 0 because it is nothing more than zero.
0.999999999999... then should be 1.0000... it is not 9.0000..., it is more than that. I think that the confusion comes about because the numbers start over then.
does anyone see what i am saying?
I don't understand what you're saying. :)
Why does it have to be 0 or 1? Can't it just be satisfied being .99999999?
because it goes on forever
What is the width of a single point in carteisan space?
1 - 0.9...
So 0.0...1 is the difference between 1 and 0.9.... So no, 0.9... is not equal to 1. And 0.0... is equal to 0 only if there are no significant digits after the 0s.
The real problem is...
1/9 is 0.1...
2/9 is 0.2...
3/9 is 0.3...
...
8/9 is 0.8...
But 9/9 is not 0.9...
I guess a single point is not evenly divisble by an odd number. Funny how that works. There is no mystery here people, move on. :)
actually i take that back, i am trying to figure out why .99999... = 1
I don't understand why, but in all the threads that i read the people that said .9999... is not equal to 1 had really bad arguments. So i am convinced that .9999... = 1.
Someone please tell me why?
who says you have to round?
Say I wanted to go from here, sitting at my computer as usual, to the other side of the room. I would walk to the center of the room (half the distance), then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance...................
It's recurring.
OK, I see what you're getting at. I like to deal in what I can use practically, and for all practical purposes .99999 forever = 1.
Even when dealing with limits, the number approaches 1 and would be treated as such.
Yeah, but are you paper thin or will your belly cross the limit? :)Quote:
Originally posted by markman
who says you have to round?
Say I wanted to go from here, sitting at my computer as usual, to the other side of the room. I would walk to the center of the room (half the distance), then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance, then half the remaining distance...................
A point has no size though. The only property it has is location.Quote:
Originally posted by CiberTHuG
What is the width of a single point in carteisan space?
1 - 0.9...
So 0.0...1 is the difference between 1 and 0.9.... So no, 0.9... is not equal to 1. And 0.0... is equal to 0 only if there are no significant digits after the 0s.
The real problem is...
1/9 is 0.1...
2/9 is 0.2...
3/9 is 0.3...
...
8/9 is 0.8...
But 9/9 is not 0.9...
I guess a single point is not evenly divisble by an odd number. Funny how that works. There is no mystery here people, move on. :)
From a practical standpoint, 0.9... is 1, but the issue is, a single discrete point can not be divided an odd number of times in an even base system. So we have a representation error. There is no mystery here.
It does have a size. It is infinately small. If you can measure infinity in any representation, then you can measure infinitely big and small. And since you can have an infinitely big number of 9s after the decimal, then you can describe an infinitely small point. :)Quote:
Originally posted by sail3005
A point has no size though. The only property it has is location.
These aren't my rules.
Consider a non-even base system then. I reckon it would still end up that with a radix of X, 0.XXXXXXXXX recurring == 1.
But the dictionary saysQuote:
Originally posted by CiberTHuG
It does have a size. It is infinately small. If you can measure infinity in any representation, then you can measure infinitely big and small. And since you can have an infinitely big number of 9s after the decimal, then you can describe an infinitely small point. :)
These aren't my rules.
Quote:
A dimensionless geometric object having no properties except location.
Yes if you can have 0.999 reccurring you can have 0.000...001, but 0.000...001 == 0.
Do programmers all get this way at some time, where simple issues get challenged logically, and your brain explodes because you wasted your life trying to prove an apple is a banana??
:confused: :p
So, you are saying it is the same on both ends?Quote:
Originally posted by HarryW
Yes if you can have 0.999 reccurring you can have 0.000...001, but 0.000...001 == 0.
Now, just to clear this up. This has nothing to do with rounding right? You are saying that 0.999.... and 1 are the EXACT same thing, correct?
So then does this basically have to do with the definition/use of infinity?
Well, from a pratical standpoint 0.0...1 == 0, but from an absolute standpoint 0.0...1 is exactly 0.0...1 away from 0.
And no, I'm wrong. It isn't an odd division in an even base system, it is an division of a number that will not even factor into the base system. So in decimal, you have the same problem with 3, 6, 7, and 9. I would imagine in octal, you would have the same problem with 3, 5, and 7, and in hexidecimal, you would have the same problem with 3, 5, 7, 9, 11, 13, and 15.
0.999 <> 1
0.999... is a percentage. Only one object in an enormous population does not conform to the test. You can not have 0.9999
You can measure what you do have against what you could have, and arrive at the conclusion you have 0.999... % of that potential.
:)
It is safe to say that 0.9... is the EXACT same thing as 1. The problem is in the representation. More times then not, when you encounter 0.9..., it is a misrepesentation of 1.Quote:
Originally posted by sail3005
Now, just to clear this up. This has nothing to do with rounding right? You are saying that 0.999.... and 1 are the EXACT same thing, correct?
1/9 + 8/9
0.1... + 0.8...
0.9...
Clearly, that should've been 1, not 0.9.... An error introduced by the circumstances (division of 9 in base 10).
but a population is finite, i am talking about something infinite. How do the properties of infinity affect the problem?Quote:
Originally posted by rjlohan
0.999 <> 1
0.999... is a percentage. Only one object in an enormous population does not conform to the test. You can not have 0.9999
You can measure what you do have against what you could have, and arrive at the conclusion you have 0.999... % of that potential.
:)
I think the fact that apple=banana has been clearly established, so we really don't need to bring THAT up again, now do we???Quote:
Originally posted by rjlohan
Do programmers all get this way at some time, where simple issues get challenged logically, and your brain explodes because you wasted your life trying to prove an apple is a banana??
:confused: :p
:)
Whether or not apple == banana depends on which language you use. ;)
Infinity is an abstract concept probably introduced by mathematicians to prove theories and rules, which look good when you assume that a population in infitine. But in practical terms, we always assume an approximation. You can not measure infinity my definition that infinity is immeasurable, so what is the problem, anyway? :pQuote:
Originally posted by sail3005
but a population is finite, i am talking about something infinite. How do the properties of infinity affect the problem?
if (apple==banana) {
me.implode
}
So has this helped, or are you just sick with us?
A little. So, what you are saying is that .99999... is equal to 1, depends on how you came up with .99999?Quote:
Originally posted by CiberTHuG
So has this helped, or are you just sick with us?
But also, if .9999... = 1, then what represents the closest thing to 1 that is not 1 and is less than 1?
0.999....etc is NEVER = 1. You just assume 1 as an approximation, because it serves your interests not to bother with ridiculous levels of accuracy.
What if we found out that everything we think about mathematics is fundamentally wrong. I mean I don't think that will happen, but just for the sake of argument.Quote:
Originally posted by rjlohan
0.999....etc is NEVER = 1. You just assume 1 as an approximation, because it serves your interests not to bother with ridiculous levels of accuracy.
What we've been doing up to now works for us, so I guess it wouldn't really matter much if we found out that 1 = blue and 2 = banana and 1 + 2 isn't theoretically possible.
OK, I have something real to work on and this isn't it :)
k, i pretty much agree with you and Ciberthug now, but why did kedaman, spend pages and pages saying that .999... = 1?Quote:
Originally posted by rjlohan
0.999....etc is NEVER = 1. You just assume 1 as an approximation, because it serves your interests not to bother with ridiculous levels of accuracy.
Harry also believes that .99999 = 1. Am i missing something?
If you are of the people that believe that .99999... = 1 then please answer this.Quote:
Originally posted by sail3005
But also, if .9999... = 1, then what represents the closest thing to 1 that is not 1 and is less than 1?
Who knows why the hell kedaman thinks 0.9999 = 1. :rolleyes: :confused:
He has logic-sickness...:p
A point only has a size in terms of how you define it's location. A point is an abstract concept. If you define its location as an integer, on an integer scale, it has a size of 1, I guess... :pQuote:
Originally posted by CiberTHuG
It does have a size. It is infinately small. If you can measure infinity in any representation, then you can measure infinitely big and small. And since you can have an infinitely big number of 9s after the decimal, then you can describe an infinitely small point. :)
These aren't my rules.
Well it seems open for debate. I'm not a mathematical genius so I am not going to try and justify it. If you can find the thread about it in the maths forum, there is a lot of stuff in there on the subject, and I found the most convincing arguments to be that they are equal.
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 9/9
x = 1
There you go.
Basically, those that do not believe that 1 = 0.999... are living in infinity denial.
If you are prepared to accept the concept of infinity, accept this concept.
simon, how can you evaluate anything infinitely recurring?
Why not?
I'll be awaiting your post of 1/3 in radix 10
As far as I know, if you have 10 radishes and divide them into three equal shares, you have 5 radishes each because I don't really like them that much so the other two get my share.Quote:
Originally posted by kedaman
I'll be awaiting your post of 1/3 of 10 radishes
I think there is some confusion here between equality and equivalence.
0.999........ is not equal to 1.
0.999........ can be considered equivalent to 1.