your avatar looks like the guy from a show-- uh what was it called lost cities of gold or something.. with some kid name sebastian -- and i forgot that guys name -- you know what im talkin about..?
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your avatar looks like the guy from a show-- uh what was it called lost cities of gold or something.. with some kid name sebastian -- and i forgot that guys name -- you know what im talkin about..?
rjlohan
Just because it's a recurring decimal doesn't mean that it doesn't exist. What about PI? Does that not exist?Quote:
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!!!
And it is not my logic, I have provided a variety of different sites where you can obtain a variety of proofs that 1 = 0.999... so I don't know what the problem is.
Keep clinging to "You can't do maths on an infinite number" bollocks all you like but it's not going to change a thing.
With 2/2, The remainder can be 0, or 2, or 4, or 2n. The proper way is for itQuote:
Originally posted by 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
to be 0. but thats why i said "Forced" remainder. Obviously, 1
times 2 is 2, but if we instead wanted to say 1.0 times 2 is 2.0.
that is certainly valid, and we can also note that 0.9 times 2
plus .2 is 2.0, which in turn could be viewed as 2.0 divided by 2
is .9 with a remainder of .2, which then leads into the series.
I wonder how many different proofs it's going to take until people actually accept the truth?
Simon they aren't proofs.Quote:
Originally posted by simonm
I wonder how many different proofs it's going to take until people actually accept the truth?
They're people trying to be clever, and proving something thats obviously wrong.
Like its possible to prove a bumblebee can't fly.
GlenW
Oh right, they're so wrong that you can obviously point out their flaws can you?Quote:
Simon they aren't proofs.
They're people trying to be clever, and proving something thats obviously wrong.
Do you actually have any reason stronger than misdirected intuition to reject thise proofs?
Stop the rhetoric and let's see some sound arguments.
Put up, or shut up! :p
The biggest flaws in the arguments are when statements like;
0.333...... = 1/3
are made.
0.333.... can be considered to be equivalent to 1/3 but it cannot be said to be equal.
So all the other crap in these 'proofs' is irrelevant, because, as far as I can see, they use this mis-interpretation of equivalence somewhere very early on.
GlenW
Err, no. They can be considered equal. Why?Quote:
0.333.... can be considered to be equivalent to 1/3 but it cannot be said to be equal.
Because 0.333... is the decimal notation for an infinite series:
3/10 + 3/100 + 3/1000 + ...
All mathematical texts I have read, contrary to Guv's assertions, suggests that the sum of an infinite series does equal it's limit (if that series converges towards a limit). It does not approach it yet never reach it, it actually equals it.Quote:
...the sum of an infinite series is equal to the limit of its partial sum, if this limit exists (if it does not exist, the series has no sum.) Also, an infinite sequence converges to L if the limit of its term is L. Furthermore, the sum of the series is also equal to L.
Those who disbelieve that fact need to go away and look up a maths site.
FIND ONE MATHS SITE THAT SAYS THAT THE SUM OF AN INFINITE SERIES DOESN'T EQUAL IT'S LIMIT.
There are plenty that say that it does, just look at any of the links I provided or find your own if you don't like them.
This one explains the use of limit and mentions that the sum calculation is never reached.
GlenW
I'm sorry but you've read it wrong:Quote:
...the sum calculation is never reached.
It is saying that we can't physically add an infinite number of terms in a finite amount of time but we can say, despite this physical limitation, that the sum of it's series is it's limit.Quote:
In our case lim( Sn ) = 2. Since this limit exists, we say that the sum of the series is 2, even though we can't really "do the sum."
The link you posted says this at the end:
If the sum of a convergent infinite series did not equal it's limit, there would be no way out of Zeno's paradox. Motion would be impossible. Since motion is possible, we can deduce that there is a way out of Zeno's paradox and therefore the sum of an infinite series can equal it's limit.Quote:
Our argument about taking smaller and smaller steps toward the wall is really due to the Greek philosopher Zeno. He imagined an arrow flying towards its target and argued that since it would never reach it, that no motion was possible. What is the flaw in his argument?
I think the important bit here is 'we can say'.Quote:
Originally posted by simonm
but we can say, despite this physical limitation, that the sum of it's series is it's limit.
Not 'it is' we can just say it is.
These numbers are representations not actual real things. (notice I didn't say real numbers)
Some fractions cannot be stated as decimals, so a reprsentation is needed.
I like totally pointless arguments like this.:D
Just a similar thought, from an argument I heard that got quite heated.
What time follows 23.59.59
Is it 24.00.00 or 00.00.00
I have no real opinion.
I believe that 24.00.00 exists, but it is infinitesimally small.
But does 00.00.00 exist.Quote:
Originally posted by Bonker Gudd
I believe that 24.00.00 exists, but it is infinitesimally small.
If it does it will be infinitesimally small as well but where will it be?
:confused: :eek:
look at it this way--
.9999....
makes just about as much sense if you were to flip the digits over the decimal like this
....9999.0
Since 24.00.00 is infinitely small, and someone mentioned infinity cant be applied to real life, how can that be
because lifes a vulgar 5-letter word and then you die -- in other words whos going to be around to test for infinity? lol:eek:
Why did you put the "s" on the of life is only a four letter word. What does this have to do with .999 anyway?Quote:
because lifes a vulgar 5-letter
Mendoza! You're the first one to work out who he is... :pQuote:
Originally posted by MegaMan
your avatar looks like the guy from a show-- uh what was it called lost cities of gold or something.. with some kid name sebastian -- and i forgot that guys name -- you know what im talkin about..?
haha i recognized that guy cuz well my friend has every tape of that damn cartoon and made me watch every episode.. it was kind of cool until they got that dumb flying bird thing. and ran into some aliens.. lol:eek:
it was supposed to be "life's a 5-letter vulgar word" but you totally misunderstood what i wrote.. a 5-letter vulgar word --Quote:
Why did you put the "s" on the of life is only a four letter word. What does this have to do with .999 anyway?
b-i-t-c-h -- DUH..
lifes a ***** and then you die ---whos going to be around to test for infinity... that what it was ---i cant believe i had to explain that to you! lol
:p
In regards to this message:
Quote:
Since 24.00.00 is infinitely small, and someone mentioned infinity cant be applied to real life, how can that be
and thats what it has to do with .999.. lol
Hope this hasn't been repeated:
Let's say you have 0.999999999999999999999999999999999999999999999999999999999 = x
(assume that long number above to be an infinite number of 9s)
multiply by 10
9.999999999999999999999999999999999999999999999999999999999 = 10x
now do this:
9 = 10x - x
9 = 9x
1 = x
so 0.99999999999999999999999999999999999999999999999999999999999 = 1
Tadaaa...! :confused:
uh no. why does it matter if you multiply it by 10?
9 = 9x is the same as saying x = 1 not x = .99999..
1=1x, 2=2x, are only true when x =1. so .9999.. is not in the part of the solution set, only 1 is.Quote:
(assume that long number above to be an infinite number of 9s)
multiply by 10
9.999999999999999999999999999999999999999999999999999999999 = 10x
:rolleyes:
Exactly. It doesn't matter what you multiply by.
So, obviously there are two ways to go about it. One's the correct way (my way) and the other way is the confusing and inconclusive one (yours) :)
no no.. u missed my point..
9=9x is only true if x = 1 -- you said that x=.9999.. is part of the solution set AND IT ISNT!
and you missed my point. I was working backwards, which is acceptable.
I multiplied by 10 and worked my way to 1. This is a common question, I've seen it before. and .999999999999999999999999999999999999999999999999999999999999999999999999999 is part of the solution. Seriously, read my post again.
my dear mendhak you have no point.
I was just thinking the same thing... :D :pQuote:
Originally posted by MegaMan
my dear mendhak you have no point.
The use of this little math trick is a bad manipulation of numbers, it's just one of those freak things that sometimes happen. Like helicopters flying when it should be physically impossible.
All this does is allow you to use the numeric value of x to achieve a true 9on one side, then use the variable x on the other side to achieve a true 9x. This way it comes out nice and clean. If your assuming x to be an infinite number of 9's then this problem is just rounding to 1 there not really equal.Quote:
Let's say you have 0.999999999999999999999999999999999999999999999999999999999 = x
(assume that long number above to be an infinite number of 9s)
multiply by 10
9.999999999999999999999999999999999999999999999999999999999 = 10x
now do this:
9 = 10x - x
9 = 9x
1 = x
so 0.99999999999999999999999999999999999999999999999999999999999 = 1
All this really comes down to one thing - you can't work with an infinitely long number and get a true answer, because you have to assume and round. So if your wanting exact then 1 will NEVER be = to .99999......
I saw a guy on TV make the space shuttle dissapear -
but I'm guessing there was a trick to it..
It is a clever math trick though.
...Here comes another one... :rolleyes:
joltremari
You can work with a real number containing an infinite number of decimal places. Do you know why? Because all real numbers have an infinite number of decimal places. That is why you can always find another real number between any other two real numbers.Quote:
All this really comes down to one thing - you can't work with an infinitely long number and get a true answer, because you have to assume and round. So if your wanting exact then 1 will NEVER be = to .99999......
Even 1.0 is actually equivalent to 1.000...
And, if you are really interested in learning some maths, there are a whole host of other proofs that demonstrate that 1 = 0.999...
Just scroll back through the thread and find the links I posted. One of the links I posted actuall provides about six different ways of prooving it.
Agree to disagree?, with math aside, in my opinion if you are going to use the symbol '=' then the value should be the same on both sides. And a 1 and a bunch of 9's are not the same - no matter how many different ways it can be proved.
If a persons paycheck was figured using this method I'll bet it would be different, how many company's would round $2000 to $1999.98 (or .99) instead of leaving it rounded to 2000....
anyway...it really just matters how accurate you need to be, and what .9999999... represents - such as does it represent just a number on a piece of paper or a distance. I guess depednding on that then you can manipulate it to become whatever you want it to be.....
interestingQuote:
Everything I say is either loose interpretation of dubious facts or idle speculation rooted in irrational sentiment.
joltremari
You can believe anything you want to believe...Quote:
Agree to disagree?
Well, if you want to push the laws of maths to one's side, you can believe anything you want.Quote:
...with math aside, in my opinion if you are going to use the symbol '=' then the value should be the same on both sides. And a 1 and a bunch of 9's are not the same - no matter how many different ways it can be proved.
Would you argue that 14/2 <> 7 ? The look different, don't they?
We're not talking about rounding anything. There are an infinite number of nines and they are not rounded attall otherwise it will be less than one.Quote:
If a persons paycheck was figured using this method I'll bet it would be different, how many company's would round $2000 to $1999.98 (or .99) instead of leaving it rounded to 2000....
If everybody let intuition rule their judgement over logic, where would we be now? Still thinking the earth was flat probably. :rolleyes:
Freak things that happen? So you're implying, indirectly, that all of mathematics and physics is a freak thing that just happened?Quote:
The use of this little math trick is a bad manipulation of numbers, it's just one of those freak things that sometimes happen
Look... manipulation of numbers in anyway is allowed. As long as both the sides of the "=" are the same. I showed you that. You're not willing to accept it. This is an old problem, I've seen it before. I was showing you how it was solved.
This post is not to argue or defend anything it's just to clarify the statements I made that you took wrong
First of all I was "pushing the laws of math aside", I just meant aside from all the proofs and such that you can do on a piece of paper, just the use of the = symbol.
And I didn't say anything about the numbers looking the same - 14/2 <> 7 is not the same type problem 14, 2, and 7 are not infinite numbers they have a very definate value - they they don't have an infinite number of decimal places like .9999... which you can never get to the end of. I know they have an infinite number of 0's but 0 has no value in that case, that is why we would write 7.2 instead of 7.20 it's the same thing the 0 makes no difference
Also I didn't say ALL of mathmatics and physics is a freak thing that happened, I was saying there are lots of tricks and things people can do with numbers.
Just because you can prove something with a theorem or mathmatical manipulation doesn't mean it has to be true in the physical world.
Anyway I'm not goin to defend or oppose anything, like you said I can believe anything I want to believe, and my final point is...
I see it this way:
A never ending number can not be = to a non-never ending number. .999... is infinite therefore it has no definite value, just the same as .999 is not the same as .9999, if the .9999.. used for this problem is infinite then you just keep adding another 9 each time so every one is different than the last, but 1 is not infinite therefore it has a definite value, 1 not 1.1111111... or .9999 but just 1.
joltremari
Ok, you're not pushing all the laws aside, just some of them.Quote:
First of all I was "pushing the laws of math aside", I just meant aside from all the proofs and such that you can do on a piece of paper, just the use of the = symbol.
I was picking up on what you said about refusing the accept the equalityof two numbers that look so different.Quote:
And I didn't say anything about the numbers looking the same - 14/2 <> 7 is not the same type problem 14, 2, and 7 are not infinite numbers they have a very definate value - they they don't have an infinite number of decimal places like .9999... which you can never get to the end of. I know they have an infinite number of 0's but 0 has no value in that case, that is why we would write 7.2 instead of 7.20 it's the same thing the 0 makes no difference
But we're not talking about the "physical" world. We're talking about mathematical logic (that happens to have useful application in the real world).Quote:
Just because you can prove something with a theorem or mathmatical manipulation doesn't mean it has to be true in the physical world.
What we are talking about here is the sum of a converging infinite series equaling it's limit. If it didn't, Calculus would be wrong. There would be no way out of Zeno's paradox (and there is).
The fact is, we can define and work with actual mathematical infinities and so doing gives us power to make predictions about the real world that we would not have if we did not accept these infinite concepts.
Ok, you see it that way. Your way just happens to be contrary with modern mathematics.Quote:
I see it this way:
A never ending number can not be = to a non-never ending number. .999... is infinite therefore it has no definite value, just the same as .999 is not the same as .9999, if the .9999.. used for this problem is infinite then you just keep adding another 9 each time so every one is different than the last, but 1 is not infinite therefore it has a definite value, 1 not 1.1111111... or .9999 but just 1.
Infinity wasn't the first counter-intuitive concept that mathematicians presented us with. It won't be the last. Half of us will bang on about how it can't possibly be right and refuse to accept it. The rest of us will get on with using it successfully in the real world.
I agree with you on this.....
I'm an engineering student. I've had all the Calculus and physics, etc.. (I didn't want you to think I was un-edu-ma-cated).Quote:
But we're not talking about the "physical" world. We're talking about mathematical logic (that happens to have useful application in the real world).
What we are talking about here is the sum of a converging infinite series equaling it's limit. If it didn't, Calculus would be wrong. There would be no way out of Zeno's paradox (and there is).
The fact is, we can define and work with actual mathematical infinities and so doing gives us power to make predictions about the real world that we would not have if we did not accept these infinite concepts.
I accept it for school and work reasons but I don't agree with it. For no other reason that no matter how many times I see it proved - it just doesn't make good sense to me.
And one final comment :D
Just because it doesnt make sense doesnt mean its not right :p
Perhaps, but the difference is that 1.0000 = 1, whilst 0.9999 does not... :rolleyes:Quote:
Originally posted by simonm
...Here comes another one... :rolleyes:
joltremari
You can work with a real number containing an infinite number of decimal places. Do you know why? Because all real numbers have an infinite number of decimal places. That is why you can always find another real number between any other two real numbers.
Even 1.0 is actually equivalent to 1.000...
Infinite zeros is not the same as infinite 9s....:rolleyes:
ROFLMAO.Quote:
Perhaps, but the difference is that 1.0000 = 1, whilst 0.9999 does not...
Infinite zeros is not the same as infinite 9s....
speaking of never ending 9's why is that stores sell things for 19.99$ or 29.99$ and 999.99$ i mean what is the point, add a ****ing penny.. !!
comments welcome.
Psychology - a person will see a $999.99 price tag and think "Ooo - under $1000". Same for all the others. Of course, you always get rounded up at the register, but the idea is no doubt to give the illusion of a bargain.
:)