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## #1 2013-12-30 14:38:54

hungryfornumbers
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### Does 1 = .999...

In regard to 9recurring made an account because I disagree with your math.

So you let x = 0.999...

And 10x = 9.999...

But how does subtracting x from the left side = 9x?

Why wouldn't it be: 10 = 9.999... - x

10 = 9.999... - .999...

10 = 0.999...

So 0.999 = 10 I guess.

## #2 2013-12-30 15:28:45

Agnishom
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### Re: Does 1 = .999...

Welcome to the forum!

Why wouldn't it be: 10 = 9.999... - x

10 = 9.999... - .999...

10 = 0.999...

means 10 multiplied with x

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #3 2013-12-30 18:14:44

bobbym

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### Re: Does 1 = .999...

Hi hungryfornumbers;

You did not do the standard demonstration.

x = .999...
10 x = 9.999...

10 x = 9.999...
-  x = 0.999...
-------------------
9 x = 9

x = 1

In regard to 9recurring made an account because I disagree with your math.

You will not find any math forum on this side of heaven that will say anything else.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #4 2013-12-30 22:32:08

Agnishom
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### Re: Does 1 = .999...

You will not find any math forum on this side of heaven that will say anything else.

There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.

Last edited by Agnishom (2013-12-30 22:42:40)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #5 2013-12-30 22:36:53

bobbym

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### Re: Does 1 = .999...

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

The emphasis here should be on "dreamt of", as Hamlet is pointing out how little even the most educated people can explain.

I hope someone remembers that the next time we are discussing something strange.

Anyways, .999... = 1 because I said so. I bet he will never get that from another forum.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #6 2013-12-30 22:43:39

Agnishom
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### Re: Does 1 = .999...

Okay, I edited it. Did you know that an established member in here used to or does think that 0.999... does not exist?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #7 2013-12-30 22:51:55

bobbym

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### Re: Does 1 = .999...

There have been a few such members.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #8 2014-01-07 17:17:08

Photon
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### Re: Does 1 = .999...

My post was deleted and this topic name changed.

Do you know what happened?
If you can't find it then no problem. I have the original is still open on my laptop so I can repost it.

Thanks.

## #9 2014-01-07 20:50:10

bobbym

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### Re: Does 1 = .999...

Hi;

You can repost it as I have no clue what happened. Please edit post #8 and put it in there. Then I will delete this one. I will try to rename the thread. Renamed it as best as I could, I do not remember the exact name.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #10 2014-01-07 23:31:25

Agnishom
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### Re: Does 1 = .999...

Hi photon,

What did you post?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #11 2014-01-07 23:52:41

bob bundy
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### Re: Does 1 = .999...

hi Photon,

Welcome to the forum.

I don't know how that happened either .... not me .... I cannot rename posts.  I have checked your account and you have two posts recorded but only one (number 8 here) is showing.  Mystery.

Now we are all keen to know what went missing.

#### Agnishom wrote:

............  0.999... does not exist?

I am studying 'Elementary real and complex analysis' by Shilov.

In section 1.77 he proves, as a theorem from the axioms for the real number system,  that it is impossible to have an infinite sequence of 9s in the decimal form of a real number.  That would make the question meaningless.  !!!

Bob

Last edited by bob bundy (2014-01-08 00:03:59)

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #12 2014-01-08 00:36:09

bobbym

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### Re: Does 1 = .999...

Hi;

#### Kahless wrote:

vo' teH Sov batleth 'er'In

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #13 2014-01-08 00:41:51

Agnishom
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### Re: Does 1 = .999...

Could you Please post the proof and the book(if possible)?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #14 2014-01-08 01:19:10

bob bundy
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### Re: Does 1 = .999...

#### Agnishom wrote:

Could you Please post the proof and the book(if possible)?

The book is as stated above.

It's not going to be easy to condense the proof.

He starts with the real number axioms.  Then he proves everything from scratch; each result then being used to help prove the next bits.  So there's a lot of work leading up to 1.77 and it would be hard to work out if anything could be left out.

I haven't studied that chapter in detail; I got the book for the chapters on complex numbers.  I'll look and see if there's an easy way I can show what he does.  I suspect it depends on the way he defines decimals, so you may not like it even when you've got the proof in front of you.

Give me a few days and I'll try to come up with something.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #15 2014-01-08 01:59:32

Agnishom
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### Re: Does 1 = .999...

Then he proves everything from scratch;

That violates Godel's Theorem

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #16 2014-01-08 05:11:13

bob bundy
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### Re: Does 1 = .999...

Good point.  When I said 'everything', I meant everything that follows in his book, rather than everything that ever was/is/shall be.

It would be silly to attempt that as you'd have to prove 'A' and also 'the converse of A'.  That would suggest inconsistency and he goes to a lot of trouble to avoid that.  (For example: he starts by proving that zero is a unique identity for addition.)

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #17 2014-01-08 15:48:09

niharika_kumar
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### Re: Does 1 = .999...

what is godel's theorem?

*You are never as good as people tell you when you win and you are never as bad as they tell you when you lose.

*Everything happens for a reason,even if we are not wise enough to see them....oprah winfrey

## #18 2014-01-08 20:46:46

bob bundy
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### Re: Does 1 = .999...

#### Niharika wrote:

what is godel's theorem?

He expressed it in mathematical logic symbols but you can roughly sum it up as in a mathematical theory there is a statement, A, that states that "A cannot be proved".

Proof.

Is the statement true or false?

Let's suppose it is false.

Then A can be proved, which contradicts the statement.  Therefore A is true.

So in the context of my discussion with Agnishom, he was pointing out that some theorems cannot be proved.

Have a look at

http://en.wikipedia.org/wiki/G%C3%B6del … s_theorems

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #19 2014-01-08 23:30:24

Agnishom
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### Re: Does 1 = .999...

Godel's theorem are the following:

First Theorem - Undecidablity
If axiomatic set theory is consistent, there exists theorems which can neither be proved or disproved.

Second Therorem - Incompleteness
There is no constructive procedure which will prove axiomatic set theory to be consistent.

 In simple words, 1. There are truths which cannot be proved or disproved.
2. You cannot prove things from scratch; you'll have to make axioms

#### bob bundy wrote:

So in the context of my discussion with Agnishom, he was pointing out that some theorems cannot be proved.

#### bob bundy wrote:

When I said 'everything', I meant everything that follows in his book, rather than everything that ever was/is/shall be.

Sorry, that was not what I am telling. I was reffering to the Second Theorem. He cannot even prove everything in his book from scratch because it is impossible. There has to be axioms somewhere.

The second theorem was the main reason for the cancellation of the Hilbert's program.

Last edited by Agnishom (2014-01-08 23:34:10)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #20 2014-01-09 02:31:12

bob bundy
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### Re: Does 1 = .999...

hi Agnishom,

My link did work but now doesn't.  ???  I have found the article again and corrected the link.  At the moment it works.

I didn't say he proves everything from scratch.  I said

He starts with the real number axioms.  Then he proves everything from scratch;

I believe this is much the same as what you are saying.

According to Wiki his two theorems apply to theories other than set theory too.  It's a long time since I did this at University, but that was how it was introduced then too.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #21 2014-01-09 08:48:57

ShivamS
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### Re: Does 1 = .999...

How are you liking Shilov's book? On my first read, it seemed like a not very good book.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes

## #22 2014-01-09 20:25:31

bob bundy
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### Re: Does 1 = .999...

hi ShivamS

I'm reading it on a Kindle so the formulas are a bit  small for my eyes.  It's a tough read but the book was highly recommended and it was only £7-ish.

I've only had it a few days.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #23 2014-01-10 00:14:58

niharika_kumar
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### Re: Does 1 = .999...

thank bob and agnishom.

*You are never as good as people tell you when you win and you are never as bad as they tell you when you lose.

*Everything happens for a reason,even if we are not wise enough to see them....oprah winfrey