3/A = q³
it must be ... surely ... beyond the shadow of a doubt ... probably ... errrm ...
:rolleyes:
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3/A = q³
it must be ... surely ... beyond the shadow of a doubt ... probably ... errrm ...
:rolleyes:
There is no absolute value that is closest. If you are dealing with finite accuracy, it would be 0.999... up to however many digits you have. When you have infinite digits, though, you have infinite accuracy, and as such there is no longer a 'closest to' just as there is not a 'farthest from'.Quote:
Originally posted by sail3005
Ok, i am prepared to believe that .999... is equal to zero, if someone answers this question.
What is the number closest to 1, that is not equal to 1 and is less than 1?
WHY Won't anyone answer that?!?!?!?!
RJ, the method using recurring numbers is part of a proof that any recurring number is rational. It's not an undefined number, it's rational.
sail3005
You're not going to get a satisfactory answer I'm afraid.Quote:
Ok, i am prepared to believe that .999... is equal to zero, if someone answers this question.
What is the number closest to 1, that is not equal to 1 and is less than 1?
WHY Won't anyone answer that?!?!?!?!
George Cantor prooved that there are uncountably many real numbers and so you cannot count sequantially through the real numbers.
Cantor's "Uncountability" proof can be found on this page:
Godel
'Zactly. Like the Av Keddie dear :) S'very cool.Quote:
Originally posted by kedaman
it doesn't :p
Look. 0.999 . . . . = 0.999 . . . .
End of story.
:p
Thanks Vicky :)
I'm not up on all these terms, I'm merely going on what I see as simple 'logic'. The number 0.11111.... can not be defined simply because of the fact that the traling 1s are infinte. Infinity has no definition, or bounds.
The number 1/9 on the other hand is a concept we can use. I'm simply saying that 1/9 <> 0.1111.... because 0.11111 is not a definite number. It is infinite.
rjlohan
Go tell that to Achimedes, Newton, Cantor and many other of the great mathematicians who used a definition of infinity in a logical context.Quote:
No it's not. Infinity can not be defined, so you can't use it in a logical context.
Similarly, you can't use infinite numbers as part of a mathematical equation to arrive at an absolute equality. You can get an approximation, and that's all you ever need.Quote:
Originally posted by simonm
sail3005
You're not going to get a satisfactory answer I'm afraid.
George Cantor prooved that there are uncountably many real numbers and so you cannot count sequantially through the real numbers.
Cantor's "Uncountability" proof can be found on this page:
Godel
Well this is a technical subject RJ. You can't get away from the fact that, technically, recurring numbers are rational. Or, 'definite', if you like.
Infinities cause a lot of problems when you want to look for proofs, but you can often eliminate them from the issue with a little effort and carry on unburdened by them.
I think many of those people had some pretty stupid ideas at times. Just because something they said was genius, doesn't mean it all was. It's all very fascinating philosophically, but I don't think in this case that something like that is true. BTW: I have no idea what exactly you are referring to.Quote:
Originally posted by simonm
rjlohan
Go tell that to Achimedes, Newton, Cantor and many other of the great mathematicians who used a definition of infinity in a logical context.
The fact that infinity by definition has no limit should be enough to convince anybody to see that you can't use that number. You can't just multiply it by 10, because that assumes that there was some digit somewhere down the track, 1billion places after the d.p if you like at which to begin such an equation. And since there isn't, you can't.
1/9 is a rational number. 0.1111.... is an approximation of that number. If you wish to assume that number is infinite, which it is, then you can no longer use it in a mathematical context, except to approximate.Quote:
Originally posted by HarryW
Well this is a technical subject RJ. You can't get away from the fact that, technically, recurring numbers are rational. Or, 'definite', if you like.
Infinities cause a lot of problems when you want to look for proofs, but you can often eliminate them from the issue with a little effort and carry on unburdened by them.
Here's another puzzler :
When and how do you know a number has an infinite number of 9's after the comma ? There is a certain uncertainty about the concept 'infinity'.
How many times does a pattern have to recurr before you can conclude that it will recurr an infinite amount ?
What if the pattern breaks after the 1.000.000.000.000.000.000.000th digit (instead of a 9 an 8) ?
You dismiss it on the basis of logic but what if your logic theorem is wrong ?
Are you ever a 100% sure about your statements regarding infinity ? If not, how much of an approximation do you think you hold ? IS it enough to accurately predict or not ?
In this case the logic of long division is enough to prove that. And shut up will ya - it's confusing enough in here... :pQuote:
Originally posted by Wally Pipp
Here's another puzzler :
When and how do you know a number has an infinite number of 9's after the comma ? There is a certain uncertainty about the concept 'infinity'.
How many times does a pattern have to recurr before you can conclude that it will recurr an infinite amount ?
What if the pattern breaks after the 1.000.000.000.000.000.000.000th digit (instead of a 9 an 8) ?
You dismiss it on the basis of logic but what if your logic theorem is wrong ?
Are you ever a 100% sure about your statements regarding infinity ? If not, how much of an approximation do you think you hold ? IS it enough to accurately predict or not ?
Sorry RJ, but I just don't think you know what you're talking about ;)Quote:
Originally posted by rjlohan
1/9 is a rational number. 0.1111.... is an approximation of that number. If you wish to assume that number is infinite, which it is, then you can no longer use it in a mathematical context, except to approximate.
Is it ?
How can you be sure that the 1.000.000.000.000.000.000.000.000.000.000th digit is the same as the 1000.000.000.000.000.000th ?
The point is that you work with approximations. It's no use guessing the 1.000.000.000.000.000th digit of a number if you use the rounded version in your common calculations.
While it makes up for an interesting philosophical debate it's simply impractical to be used on a daily basis.
The approximations work just fine.
Hear hear. Most of what they said doesn't make sense at all, but they say one intelligent thing, and suddenly, their geniuses, and everything they say must be right :rolleyes: I wish my life was like that.Quote:
Originally posted by rjlohan
I think many of those people had some pretty stupid ideas at times. Just because something they said was genius, doesn't mean it all was.
No doubt :p, but I'm yet to be convinced that 0.99999... = 1Quote:
Originally posted by HarryW
Sorry RJ, but I just don't think you know what you're talking about ;)
Well you'd have to say something intelligent first :pQuote:
Originally posted by rinoaheartilly
Hear hear. Most of what they said doesn't make sense at all, but they say one intelligent thing, and suddenly, their geniuses, and everything they say must be right :rolleyes: I wish my life was like that.
Quote:
Originally posted by rinoaheartilly
Hear hear. Most of what they said doesn't make sense at all, but they say one intelligent thing, and suddenly, their geniuses, and everything they say must be right :rolleyes: I wish my life was like that.
Mine is. :)
.....I think.... :confused:
:p
Do me a favour. Shut up!Quote:
Originally posted by rjlohan
No doubt :p, but I'm yet to be convinced that 0.99999... = 1
Sorry, but stupid arguements like this REALLY get on my nerves :mad: :p It's totally pointless
STFU Rj :D you heard the girl ;)
The funny thing is that most of us will probably call it "enough precision for the calculations at hand" right after the 50th digit because, quite frankly, we can't be bothered with the cumbersome process of determining where exactly we should stop refining the number.
In essence :
Even if 0.99999... equals 1 we still would be using 1 in our calculations because it's the easiest way out.
We accept a certain amount of inaccuracy because our calculations don't require that much accuracy.
Philosophically you could argue until you're blue in the face but in reality you use approximations because you need to be arbitrary and there is no room for pointless arguing about an accuracy you will never achieve and most certainly never use in the first place.
Me too. :mad:Quote:
Originally posted by rinoaheartilly
Do me a favour. Shut up!
Sorry, but stupid arguements like this REALLY get on my nerves :mad: :p It's totally pointless
...they distract me from real work... :p
Ked - not like you to take that line... :p ;)
rjlohan
Well, each of those mathematicians used infinity in a logical fashion and that is what they are famous for.Quote:
I think many of those people had some pretty stupid ideas at times. Just because something they said was genius, doesn't mean it all was. It's all very fascinating philosophically, but I don't think in this case that something like that is true. BTW: I have no idea what exactly you are referring to.
Archimedes sliced up objects into infinitely small slices to acurately calculate their volume.
Newton used infinitely small divisions for the basis of calculus.
Cantor founded modern set theory and formalised the way with which we can think about infinities.
1) That can't be done, because by dividing an object, you are setting limits on the size of the divisions, no matter how small you want to make it, and hence it is no longer infinity.
2) Calculus quite often only seeks to approximate some value, it is not an equality statement.
3) That's luverly... so what? :p I've never heard of him anyway...
:p
I can't believe this conversation is still going on. There is no big mystery here people. It is cut and dry, just look at it.
0.9... is not equal to 1, but in most cases when you encounter 0.9... it is a misrepresentation of 1 introduced by system we are using.
And there is no debate, there is no thinking about it. It's like gravity. It works, and no matter how much you disbelieve it, you still fall down.
Yes it is. It is absolutely an equality statement. It is precise. It's not an approximation, that's why it was such a big deal.Quote:
Originally posted by rjlohan
2) Calculus quite often only seeks to approximate some value, it is not an equality statement.
I don't know about you, but I had Wing-Chun tonight, and it's now 1am ... I'm too buggered to go research Calculus right now... :p
Cyberthug
You are talking nonsense.
All proofs point to the fact that 1 = 0.9999...
Deal with it. I did (and god knows, I needed a lot of convincing).
Quote:
Originally posted by simonm
Cyberthug
You are talking nonsense.
All proofs point to the fact that 1 = 0.9999...
Deal with it. I did (and god knows, I needed a lot of convincing).
If that was true, there'd be no argument...:rolleyes:
Perhaps you're the one who should be 'dealing with it'...
It's perfectly interesting to imagine that that 'proof' displayed before leads us to the fact that 0.999... = 1, but it doesn't you assume too much about the derivation of the equations therein. You can't do math on an infinite number, that just doesn't make sense.
I still think this is the problem.Quote:
Originally posted by GlenW
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.
Yeah, that too.Quote:
Originally posted by GlenW
I still think this is the problem.
Ok, I'll throw this one out there - how can it be an equality, when infinity does not exist as a definite limit?Quote:
Originally posted by HarryW
Yes it is. It is absolutely an equality statement. It is precise. It's not an approximation, that's why it was such a big deal.
One of the facts about the real number line is it's uncountability.
Take any two real numbers and you can always find another (infinitely many) real number in between them.
If you have two, seemingly different real numbers, and you cannot find a real number between them, then they are infact the same number.
But you can find a real number between them - you just go a single step further down the chain of 9s.
* :rolleyes: *
It seems to me that you are simply refusing to accept the notion of infinity and assuming that, because you don't accept it, it doesn't exist.Quote:
But you can find a real number between them - you just go a single step further down the chain of 9s.
You can't go another step down the chain of nines.
That means an infinity of nines follow. You can't just add another one because you've already gone to infinity. That's the point!Code:_
0.9
Variations on this topic have been argued at VB Forums several times. One question which keeps coming up relates to the number less than one which is closest to one. There is no such number. Cantor, Dedekind, or somebody proved a more general statement than that, which is applicable.
Cantor might have made some statement about a real number being represented by an infinite number of decimal digits, but I doubt that he ever based any of his proofs on operations involving the decimal system of notation.
It is just not valid to set a value equal to its limit, although is it is sometimes stated that doing so for computational purposes will not result in erroneous results.
Consider the following two limits.
Limit(1 + 1/n) is one as n grows without bound.
Limit[ (1 + 1/n)^n ] is e (approximately 2.7182818) as n grows without bound.
If the limit value for (1 + 1/n) is used in the latter expression, this implies that 1^n = e, or that the second limit is one rather than e. Neither of these two alternatives is correct.
Do you propose picking and choosing which values are equal to their limits and which are not? Do you claim that in some contexts it is OK, but in other contexts it is not? Sometimes you allow it, at other times you do not.
You can look up the formal definition of a the limit of a series with an unbounded number of terms in any good college text. It is a bit cumbersome, but essentially states that the difference between the sum and the limit becomes arbitrarily small. It does not define the difference as zero.
There is never a statement like: When n equals infinity, the sum of the series equals the limit. Such a statement is invalid. As far as I know, formal texts on calculus and analysis do not use the term infinity. They use statements like grows without bound.
The following proof would never be considered valid by a formal mathematician.
x = .9999. . .
10x = 9.9999. . .
10x - x = 9
9x = 9
hence x = 1
One or both of the bolded statements are not valid operations. One must define such operations using limits or other formal methods, rather than relying on intuition or common notions.
It can be shown that there are many numbers between .99999. . . and one. It should be noted that it is probably not valid in some contexts to use decimal notation as the basis for mathematical proofs. This is probably one such context.
Recurring decimal .9999 is 9/10 + 9/100 + 9/1000 . . .+ 9/10^n
Recurring Hex .FFFF is 15/16 + 15/256 + 15/4096 . . .+ 15/16^n
The above two series are not equivalent, although one is the limit value for both. Using decimal equivalents, the first few sums are the following.
.9000 — .9375
.9900 — .99609375
.9990 --- .99975586 . . .
.9999 — .99998474 . . .
The above clearly indicates that for any finite value of n, the sum of the Hex series is always greater than the sum of the decimal series and less than one. Hence, the sum of the Hex series is always between the sum of the decimal series and its limit.
There seem to be people who post at the VB Forums who believe that there is a place called infinity where magic takes over and mathematical logic is no longer valid. Nobody has ever traveled there to see what happens. There are some common notions like parallel lines meet at infinity or the sum of an infinite number of terms is equal to the limit, but mathematicians do not agree with these notions.
For every value of n that we can investigate, the hex series is greater than the decimal series and less that one. Do you really believe that when you get to the land of Oz (infinity), the hex series will no longer be greater than the decimal series? If they both become equal to one, what happens if you add one more term? Do they both exceed one? Does some monster keep you from adding one more term?
As for me (and many serious mathematicians), recurring decimal .99999 is equal to recurring decimal .99999, and recurring Hex .FFFF is equal to recurring Hex .FFFFF and both have one as the limit value. Neither is ever equal to one, and the Hex series is always between the limit and the decimal series. There is a huge (probably unbounded) number of series whose sums are between the sum of recurring nines and the limit value.
Just as parallel lines never intersect, asymptotes never meet their limit lines, and the sum of an infinite series never equals its limit. Follow the parallel lines or asymptotes for light years, billions of light years, et cetera, the parallel lines never intersect and the asymptotes do not touch their limit lines. Sum the series for millions, billions, trillions, et cetera of terms, there is always some infinitesimal difference between the sum and its limit
Why assume that the above situations somehow change at or on the way to some Land of Oz at a place called infinity? When you get there, is it impossible to go further? Do the parallel lines terminate there? At infinity does one of the parallel lines make a right angle turn to meet the other? Do both the parallel lines gradually bend toward each other? Do they start bending toward each other before you get to infinity or afterwards? At infinity can you no longer add even one more term to a series? What prevents you from adding one more term? If you can add one more term, do you exceed the limit?
There may be text books written for pre-college courses which are informal in some of their statements. No modern text written for serious mathematicians will claim that it is valid to set the sum of a series to its limit.
I think I have seen instances in which a text made some statement like: Erroneous values will not result from use of the limit for computational purposes. I think it is sometimes valid to define a function as equal to a limit for a particular value of the independent variable.
No the point of infinity is it doesn't stop. There is no limit to the number of 9's. So you can't be there.......Oh! dear. I'm lost sorry. byeQuote:
Originally posted by simonm
You can't just add another one because you've already gone to infinity. That's the point!
Crap and double crap. I'm accepting it. I'm accepting it as an undefinable limit on a quantity.Quote:
Originally posted by simonm
* :rolleyes: *
It seems to me that you are simply refusing to accept the notion of infinity and assuming that, because you don't accept it, it doesn't exist.
:rolleyes: :rolleyes:Quote:
Originally posted by simonm
You can't go another step down the chain of nines.
That means an infinity of nines follow. You can't just add another one because you've already gone to infinity. That's the point!Code:_
0.9
And your first statement that they are equal because there is no number in between can only be proved by assuming that at some point, you will have reached infinity and deduced there's no more numbers. But infinity determines that you can never reach that point, hence you can't claim there are no more numbers, because there are - ALWAYS.
I know that's the point. But do you?
Guv - too much to read, break it down for us tired souls in Oz... :p
Thank christ there's at least one sane person aboot. :DQuote:
Originally posted by GlenW
No the point of infinity is it doesn't stop. There is no limit to the number of 9's. So you can't be there.......Oh! dear. I'm lost sorry. bye
I gather you're on my wavelength here - you got my point.
Guv's last post is very good.Quote:
Originally posted by rjlohan
Thank christ there's at least one sane person aboot. :D
I gather you're on my wavelength here - you got my point.
True. :)Quote:
Originally posted by GlenW
Guv's last post is very good.
The bit about the x = 0.999... , 10x = 9.999 is a point I raised earlier, although without the mathematical know-how to make it sound like I knew what I was on about... :p
Guv
No it can't be shown.Quote:
It can be shown that there are many numbers between .99999. . . and one. It should be noted that it is probably not valid in some contexts to use decimal notation as the basis for mathematical proofs. This is probably one such context.
Your illustration with hex notation does not prove anything because it doesn't matter that, after any number of finite steps, one is greater than the other.
Take Pi:
3.1 is rational
3.14 is rational
3.141 is rational
3.1415 is reational
...
Hence Pi is rational (which is obviously wrong).
The point is, Pi, after any number of finite steps is incomplete and a mere approximation. It is complete and exact after an infinite number of decimal places.
It is quite simple, Guv. One limit converges and the other doesn't.Quote:
Consider the following two limits.
Limit(1 + 1/n) is one as n grows without bound.
Limit[ (1 + 1/n)^n ] is e (approximately 2.7182818) as n grows without bound.
If the limit value for (1 + 1/n) is used in the latter expression, this implies that 1^n = e, or that the second limit is one rather than e. Neither of these two alternatives is correct.
Do you propose picking and choosing which values are equal to their limits and which are not? Do you claim that in some contexts it is OK, but in other contexts it is not? Sometimes you allow it, at other times you do not.
Here's a proof that I pulled from somewhere that prooves that there is no real number between 1 and 0.999... (I think it's different from Sam Finch's)
Quote:
Assuming you're right - that .999... is not equal to 1,
The number .999... + (1 - .999...)/2
1) must be greater than .999...,
2) but still less than 1.
1) Greater, because (1-.999...) is greater than zero (because of the assumption that 1 != .999...), and half of anything greater than zero is still greater than zero.
2) Less than 1, because X+(Y-X)/2 = Y-(Y-X)/2. If Y is 1 and X is .999..., then .999...+(1-.999...)/2 is equal to 1-(1-.999...)/2, i.e. equal to 1 minus something greater than 0.
So, assuming what you said (.999... not equal 1), that means .999... + (1 - .999...)/2 is closer to 1 than .999... is, contradicting the other thing you said - that 0.999... is as close as you can get without being equal (because we found another number that is even closer, but which can't be equal, unless your assumption is false.
Simon, I'd expect that response from Ked, but I'll explain it again.Quote:
Originally posted by simonm
You are talking nonsense.
All proofs point to the fact that 1 = 0.9999...
Deal with it. I did (and god knows, I needed a lot of convincing).
Infinity has to be assumed to exist. You can have an infinately large object and you can have an infinitely small object (refered to as a point in the carteisan system). Infinitely small objects exist only on paper (as does infinitely big ones) since you could never actually measure one.
0.9... is exactly one point away from 1. It is an infinitismal distance away. A singularity that is so small it can no longer be divided. Yes, such a thing may not physically exist, but neither does anything infinitely big, because when you find it, there is another step to take.
Well, in the decimal system, it is easy to group infinities in certain groups. The group between 0 and 0.5 and the group between 0.5 and 1. You've split an infinity into two equal infinities.
But something happens when you start taking thirds or ninths. You have a representation problem.
1/9 is represented as 0.1... and 8/9 is represented as 0.8.... Well, 1/9 and 8/9 should be a whole, but 0.1... and 0.8... winds up short of a whole by 0.0...1. It is infinitely close to 1, but somewhere you drop a single point. Why? Because in a decimal system, if you divide any single point into nine peices, you have split the remander into ninths again and again and again.
We simply have a representation error in this case. So in this case, it is safe to assume that 0.9... is a misrepresentation 1.
Does this prove that 0.9... is in fact equal to 1? No. There are no two numbers that are equal, ever (that is actually the basis for having numbers in the first place is that each one describes a completely unique point in the cartiesan space that can be described by exactly no other numbers). 900 is not 1000, 90 is not 100, 9 is not 10, .9 is not 1, ad infinitum.
This discussion is just mental masturbation. Every number is unique, and there is no exception. Mathematics do not adhere to the laws of physics. In other words, there are no exceptions that make the laws.
And using this logic, I can disprove infinity (the big one).Quote:
Originally posted by simonm
Here's a proof that I pulled from somewhere that prooves that there is no real number between 1 and 0.999... (I think it's different from Sam Finch's)
Quote:
Assuming you're right - that .999... is not equal to 1,
The number .999... + (1 - .999...)/2
1) must be greater than .999...,
2) but still less than 1.
1) Greater, because (1-.999...) is greater than zero (because of the assumption that 1 != .999...), and half of anything greater than zero is still greater than zero.
2) Less than 1, because X+(Y-X)/2 = Y-(Y-X)/2. If Y is 1 and X is .999..., then .999...+(1-.999...)/2 is equal to 1-(1-.999...)/2, i.e. equal to 1 minus something greater than 0.
So, assuming what you said (.999... not equal 1), that means .999... + (1 - .999...)/2 is closer to 1 than .999... is, contradicting the other thing you said - that 0.999... is as close as you can get without being equal (because we found another number that is even closer, but which can't be equal, unless your assumption is false.
Given a number x that is thought to be equal to infinity, can't I add 1? Now I have a number bigger than before.
0.9... is only absolutely equal to 1 if there is no such thing as infinity. In all other cases, it is a misrepresentation of infinity.
This is really getting tiresome now. There are any number of mathematical sites that you can go to to prove that 1 = 0.999...
Just go and learn for yourselves:
Ask Dr. Math
the sci.math FAQ
the University of Michigan math dept.
the alt.algebra help FAQ
a professor at Rowan University
Prestidigitation is not proof, just clever tricks.Quote:
Originally posted by simonm
This is really getting tiresome now. There are any number of mathematical sites that you can go to to prove that 1 = 0.999...
Just go and learn for yourselves:
Ask Dr. Math
the sci.math FAQ
the University of Michigan math dept.
the alt.algebra help FAQ
a professor at Rowan University
Check the file title in the the last URL.
If any of them are right, then that underminds the basic principle of numbers and the coordinate system, in which case, it is only a matter of time before someone "proves" that 1 is in fact equal to 2.
Cyberthug
No it doesn't. Infact, our very notion of real numbers relys on this fact and will not be undermined by it.Quote:
If any of them are right, then that underminds the basic principle of numbers and the coordinate system, in which case, it is only a matter of time before someone "proves" that 1 is in fact equal to 2.
* :rolleyes: *Quote:
Prestidigitation is not proof, just clever tricks.
Check the file title in the the last URL.
The last URL is infact very good. It provides a series of arguments that proove 1 = 0.999...
It is entitled "Fun" because it is supposed to be making calculus fun (if that's attall possible).
Thank you Keddie bachQuote:
Originally posted by kedaman
STFU Rj :D you heard the girl ;)
:eek: Hey!!! I say lots of intelligent things.Quote:
Originally posted by HarryW
Well you'd have to say something intelligent first :p
Although, I s'pose it depends on what your definition of intelligent is ;):p
Lol :p:DQuote:
Originally posted by rjlohan
Me too.
...they distract me from real work...
Ked - not like you to take that line...
OMG. What is the point of arguing about this. Like I said, 0.999 . . . . = 0.999. . . .
The End.
Diwedd.
Fini
etc.
No, it's entitled fun because the people who wrote it were doing amusing tricks to make ppl like you believe that 0.9999... = 1Quote:
Originally posted by simonm
Cyberthug
No it doesn't. Infact, our very notion of real numbers relys on this fact and will not be undermined by it.
* :rolleyes: *
The last URL is infact very good. It provides a series of arguments that proove 1 = 0.999...
It is entitled "Fun" because it is supposed to be making calculus fun (if that's attall possible).
:rolleyes:
Your logic is still based on the assumption that you can perform maths on an infinite number, which you can't, because IT DOES NOT EXIST!!!
You're harping on about how we are all denying the existence of infinity etc, when the problem is that you don't seem to understand what infinity is... :rolleyes:
Quote:
Originally posted by rinoaheartilly
OMG. What is the point of arguing about this. Like I said, 0.999 . . . . = 0.999. . . .
The End.
Diwedd.
Fini
etc.
Look, if we want to argue, we'll argue, OK?? :p
(Anyway, you're just pissed because you keep getting email notifications for a thread you don't want to be a part of.... - now, don't you regret posts that get you into those situations... :p)
That proof is ludicrous...:rolleyes:Quote:
Originally posted by simonm
Here's a proof that I pulled from somewhere that prooves that there is no real number between 1 and 0.999... (I think it's different from Sam Finch's)
0.999... is a non-definable number, hence you can't halve it, multiply it by 10 or anything else...:rolleyes:
Sorry Vicki.Quote:
Originally posted by rinoaheartilly
Do me a favour. Shut up!
Sorry, but stupid arguements like this REALLY get on my nerves :mad: :p It's totally pointless
sail3005 and participants : English isnt my first language-- but bear with me here..
You know i've thought about that half thing a million times.. from x to y there is an infinite number of halfways.. but the factor that you are overlooking is that we are slaves of time- and thus limited in our perspective and ability to understand the concept of infinity. For all practical purpose, single integer numbers are finite. that is why 1 cannot be equal to .9999... no matter how continuous that number is..
You've taken calculus right? ever heard of a class called calculus theory? in that class they try to rationalize the concepts of math and physics, of space and time. ----- Anyway I just wanted to point out that-- you are attempting to compare apples to oranges when dealing with finite and infinite numbers. Although theoreticaly speaking numbers all have the same properties-- as far as math, algerbra calculus go.. but those are all limited to third dimensional aspects.. numbers are finite because in time, they end.
When numbers dont end they are -- how do you say--
oposing the laws of time.. and thus must exist outside the scope of time--- they exceed the boundaries of the fourth dimension and therefor-- contradict everything we know about the world. Such thinking is beyond our comprehension.. but keep trying maybe you'll figure it out..
HEY AND THE LETTERS ON MY KEYBOARD are fading i just noticed.. lol
MEGAMAN
well you cant get a remainder when you divide 2 by 2.. because it is 1, the remainder is always 0.. so what was that image all about??
megaman
i noticed that the "proofs" some ppl are trying to use shows the LIMIT of .999.. the limit may equal 1 but that doesnt mean that .999... = 1 .. that is a fallacy, falsity.. whatever
megaman