0.999... = 1 debate

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Postby hunter1801 » Wed Feb 16, 2011 11:50 am

Roach412 wrote:....they will never be the same, as their value can always be adjusted by repeating the number again...and again...and again... fractals are similar example.

0.9... could be: 0.9999999999999999999999999999999
0.9... could be: 0.999999999999999999999999999999
they can be any variation of these, more 9's fewer 9's...doesn't matter. until you say "there! that's how many 9's there are", you simply do not have a real number from which to do equations with - it's an undefined limit.


Can't say I agree with that. 0.9... can't be 0.9999... or 0.99.... It is always 0.999... There are no more or less 9's at the end of any repeating string of 9's. Like I mentioned it isn't a "process". You are thinking of it as a repeating process or sequence when it should be thought of as a single number. Granted, not a solid number with a defined end, but it is still a value in "concept". A representation of something in a way.

Roach412 wrote:if you do not make a point at which the number ends, then yes, it really does not end - ever...over any amount of time space or anything. it quite literally is a race to infinity.


Can't really think of it in terms of a race, but if you do, then since they are the same they have to start at the same time. Neither is ahead or behind the other.

You can't say that one 0.999... might be different than another 0.999... by saying that one might have fewer or more 9's. You would then be assuming that one "started" sooner when numbers don't start at all to begin with. They are just numbers sitting there not going any direction in time or space. 0.999... can only be one thing, and it is the same as any other 0.999...
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Postby CivilDissent » Thu Feb 17, 2011 3:43 pm

And, all of this just goes to show that neither "science" nor mathematics is exact....blowing many collegiate "proofs" out of the water.
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Postby evasive » Fri Feb 18, 2011 12:56 am

like this. there's some light coming from the farthest star and travelling billions of lightyears. you take a bit of the thinnest black paper. compare the distances. the final distance will not be zero. not ever. you will never reach the surface. so, 0.999999....... is not 1. done.
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Postby Roach412 » Fri Feb 18, 2011 7:54 am

hunter1801 wrote:Can't say I agree with that. 0.9... can't be 0.9999... or 0.99.... It is always 0.999... There are no more or less 9's at the end of any repeating string of 9's. Like I mentioned it isn't a "process". You are thinking of it as a repeating process or sequence when it should be thought of as a single number. Granted, not a solid number with a defined end, but it is still a value in "concept". A representation of something in a way.

but that is the way math works, "as a number approaches..." either a limit or a floor, it truly is a process. without defining your range it literally, and theoretically, is still going. we apply limits to infinite numbers because in reality the human brain cannot fully grasp infinity. why else would we simplify .33333333333333... as 1/3? because it makes it easy to work with, and ABLE to be worked with. fractions which equate to infinite numbers are way to cheat, just to make it work.

hunter1801 wrote:You can't say that one 0.999... might be different than another 0.999... by saying that one might have fewer or more 9's. You would then be assuming that one "started" sooner when numbers don't start at all to begin with. They are just numbers sitting there not going any direction in time or space. 0.999... can only be one thing, and it is the same as any other 0.999...

that is exactly what i'm saying, and holds true in all math. each number is unique, even if it is the same value. 1 has the value of 1, but it is not the same as 1, it's like clones. they are different...else you cannot do a comparison - which is just plain logical reasoning.

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Postby hunter1801 » Fri Feb 18, 2011 12:28 pm

evasive wrote:like this. there's some light coming from the farthest star and travelling billions of lightyears. you take a bit of the thinnest black paper. compare the distances. the final distance will not be zero. not ever. you will never reach the surface. so, 0.999999....... is not 1. done.


Don't really know what you are trying to say there. Light traveling to and from somewhere has a fixed distance. Also, a thing piece of black paper has a fixed thickness. Not sure where that came from though. What distances are you comparing? And what "surface" are you trying to reach?

Roach412 wrote:that is exactly what i'm saying, and holds true in all math. each number is unique, even if it is the same value. 1 has the value of 1, but it is not the same as 1, it's like clones. they are different...else you cannot do a comparison - which is just plain logical reasoning.


Why would the same numbers need to be unique? Can't say I've heard of that reasoning with numbers. Two of the same numbers are just that, the same, not unique.

Edit: Another point using a more logical approach would be that, if two numbers are in fact different, then by definition there HAS to be a number between them. What number is between 0.999... and 1? There isn't one. Instead of trying to think what it would take to "get to" 1, what would it take to "move away" from 1? Any number you think of will be 1 too many and move you BEFORE 0.999...

Mentally, the only way you can say that 0.999... is smaller than 1 is if you stop repeating the 9's in your head. When in fact they don't ever stop. In order for it to be smaller than 1, the 9's have to stop. So the number will never be smaller than 1.
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Postby evasive » Sat Feb 19, 2011 1:17 am

um the number will be a finite number depending on how fast they are approaching zero. It's called algebra that is used to calculate what that number is.

2x / x with x approaching zero, will be 2.
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Postby fussnfeathers » Sat Feb 19, 2011 8:50 am

Zero is not a number, meaning it is a non-integer. You cannot make an integer like 1 equal a non-integer like zero. You cannot add, subtract, multiply or divide by it. Adding and subtracting from an integer leaves just the integer i.e. 1-0 or 1+0 always = 1, while multiplying by 0 always equals 0, no matter how many other numbers are in the equasion. If there's a 0 in there, your answer will be 0. There is no way to make 1x0 = 1, and the same with division, even in a fraction or decimal form.
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Postby hunter1801 » Sat Feb 19, 2011 12:17 pm

Well we aren't talking about zero, so that doesn't really have to do with anything, unless I'm missing your point. 0.999...is not zero. Just because it has a zero in the first digit, doesn't mean it follows all the rules of 0. You can multiply or divide with 0.X.
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Postby fussnfeathers » Sun Feb 20, 2011 9:40 am

You are, in a roundabout way. You're saying something less than zero (0.99999999999999999999 etc) is equal to 1. For that to happen, you'd have to skip 0 entirely, meaning that at some point in your equasion, SOMETHING would have to equal 0 in order to progress to 1. That's all.
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Postby hunter1801 » Sun Feb 20, 2011 10:52 am

fussnfeathers wrote:You are, in a roundabout way. You're saying something less than zero (0.99999999999999999999 etc) is equal to 1. For that to happen, you'd have to skip 0 entirely, meaning that at some point in your equasion, SOMETHING would have to equal 0 in order to progress to 1. That's all.


uh....0.9 isn't less than 0. Anything less than 0 is negative. 0.x is always bigger than 0. It is a number between 0 and 1.
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