You are not logged in.
#976 2012-06-23 10:57:16
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
I have been looking at this thread for quite a while now. I would have to state my newly developed opinion and that is that 0.999... doesn't exist.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#977 2012-06-23 16:13:58
- bob bundy
- Moderator
Offline
Re: 0.9999....(recurring) = 1?
hi Stefy,
I think you will have to define 'exist' in the context of numbers.
Isaac Azimov made a good case for the 'existance' of complex numbers that contained the challenge "Pick up that piece of chalk; now hand me half a piece of chalk." 
I can have 3 apples, or write a 3 on a piece of paper, I can hold up a piece of wood carved in the shape of the symbol 3, but I cannot hold a 3 itself. It's just an abstract concept.
So what do you mean by "It doesn't exist"?
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#978 2012-06-23 21:29:22
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
What I mean is that we cannot use the concept of 0.999... in mathematics. We know that every rational number has a unique decimal representation, so we cannot have both 1.000... And 0.999...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#979 2012-06-23 22:08:06
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
Hi;
We know that every rational number has a unique decimal representation
That is not correct.
Top of page 3:
http://www.math.cornell.edu/~kahn/countingreals07.pdf
or:
http://mas.lvc.edu/~lyons/pubs/mathreasoning2.pdf
Section 6.4
Lastly, in "Introduction to Mathematical Proofs," by Charles Roberts in section 7.3 we have,
However some rational numbers have 2 different decimal expansions.
Your statement should be, "Every irrational number has a unique and non terminating decimal expansion." 1 is not irrational.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#980 2012-06-23 22:23:13
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
It seems that guy is stating the exact opposite thing from me. I said that 0.999... cannot exist because every number has a unique decimal representation and he says that not every number has a unique decimal representation because 0.999... exists.
I have one question. How does existence/non-existence of 0.999... affect mathematics. Is it like the issue of an infinity between aleph 0 and aleph 1?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#981 2012-06-23 22:27:13
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
Hi;
You are going to have to define exists.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#982 2012-06-23 22:37:03
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
And why is that?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#983 2012-06-23 22:40:53
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
To me .999999999... is this
That is really all you need from a practical viewpoint.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#984 2012-06-23 22:51:36
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
No, I asked you why you think 0.999... has to exist? "exists" is an already defined concept.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#985 2012-06-23 22:54:52
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
I do not think it has to exist. I just can find no reason why I can not write that sum in post #983. Or why I can not sum it to 1.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#986 2012-06-23 23:03:36
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
You can. But that doesn't mean you can represent it as 0.999... .
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#987 2012-06-23 23:07:02
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
.9+.09+.009+.0009+.00009+...+
That is the same as .9999... If you agree I can then you have allowed for .9999...
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#988 2012-06-23 23:12:29
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
Okay. I was trying to see the problem from the eyes of my prof. It would seem that he is wrong.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#989 2012-06-23 23:13:41
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
Are you saying your professor does not think .999999... = 1?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#990 2012-06-23 23:17:01
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
He thinks that 0.999... doesn't exist or something like that.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#991 2012-06-23 23:20:37
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
Here is what I say. There are many skeletons in the mathematics closet. As a discretist I tell you about them everyday. But I have never given the validity of .999... = 1 a thought. It just seems too obvious. There are more important concepts to be argued than this one. In my opinion your prof. is wasting his time.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#992 2012-06-23 23:24:54
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
No, he isn't obsessed with the 0.999...=1 discussion. It is just his opinion that 0.999... doesn't exist.
I am just having a discussion on Facebook about this problem.
Last edited by anonimnystefy (2012-06-23 23:25:11)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#993 2012-06-23 23:30:19
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
It is just his opinion that 0.999... doesn't exist.
Opinions are sort of like bedbugs. They can bite ya.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#994 2012-06-23 23:33:35
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
I know.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#995 2012-06-24 00:03:23
- bobbym
- Administrator
Offline
Re: 0.9999....(recurring) = 1?
Hi anonimnystefy;
You are on facebook?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#996 2012-06-24 00:37:49
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
Yes, I am.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#997 2012-06-24 11:15:44
- Stangerzv
- Full Member
Offline
Re: 0.9999....(recurring) = 1?
0.9999999.... or 3x (1/3) doesn't exist in our human limited understanding. It is like partitioning a unit into 3. The divided units (1/3) only exist in the mathematics and not in the real world. This is what we call irrational numbers, same with the diagonal length of a square with a unit sides. We can see these irrational numbers in our life even though they actually don't exist on their own. Can you measure 1/3 or square root of 2? Square root of 2 does exist in a square but can you measure it? Never ever because they don't exist in the real world. In other words, irrational numbers only exist as complementary to others but when you take them out on their own, they do exist as a form which can't be quantify exactly into decimal system because they are endless into infinity. This is why you can never say 0.99999.....=1 because somewhere in the infinity there is a residue left when 1-0.9999....it is endless.
#998 2012-06-24 11:45:45
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
You remind me of George Y. Mathematics isn't dependent on the real world. Just because we cannot see something doesn't mean it is not there.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#999 2012-06-24 18:05:05
- bob bundy
- Moderator
Offline
Re: 0.9999....(recurring) = 1?
hi all,
I was out gardening at my Mum's yesterday so missed most of this discussion.
My point about defining 'exist' is a continuation of the idea in Stangerzv's post
We can see these irrational numbers in our life even though they actually don't exist on their own.
I don't think you can 'see' any number in this sense. You can no more 'see' a 3 than you can 'see' √3.
All numbers are just abstract concepts:
Dictionary.com wrote:
'exist'
5. philosophy a.to be actual rather than merely possible
b.to be a member of the domain of some theory, an element of some possible world, etc
Humans have invented various numbers for our convenience and mathematicians have tried to make those inventions consistent and logical. If you can call √-1 a number then you can call 0.9999999............ a number. Then you can investiagte its properties.
One property of 0.99999999999999999........... is that it behaves the same as 1. You might think that is odd but if you don't allow that then a lot of the other rules of numbers that mathematicians have constructed fall apart. So it's rather like defining x^0 to be 1. You cannot actually multiply x by itself 0 times but the rules of powers work nicely if you use this definition. Maths is full of stuff like that. You can join the crowd on this one or define your own rules. Just make sure they are consistent and logical.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#1000 2012-06-24 21:55:32
- anonimnystefy
- Real Member
Offline
Re: 0.9999....(recurring) = 1?
Did you acrually read all posts from yesterday and today?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón