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## #1 2012-09-16 08:10:51

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### 1? Or not?

My personal view- but I do not like the wording.

I (thought) it's like the "proof" of 1=2. There has to be a hidden mistake.

The problem( copied and pasted )
~~~~~~~~~~~~~~~~~
Let X = 0.999...
Then 10X = 9.999...

Subtract X from each side to give us:

9X = 9.999... - X

but we know that X is 0.999..., so:

9X = 9.999... - 0.999...
or: 9X = 9

Divide both sides by 9:

X = 1

But hang on a moment I thought we said X was equal to 0.999... ?

Yes, it does, but from our calculations X is also equal to 1. So:

X = 0.999... = 1

Therefore 0.999... = 1

~~~~~~~~~~~~~~~~~~

Common Sense: The integer 1 has a 1 in the ones place, and 0.999... has a zero.

But, (oh crack, I just got confused!)  1/3 = 0.333... and 1/3  3 =3/3=1, and 0.333...   3 =0.999...
so 0.999 would equal (1)! ( put parenthesis so not to be mistaken for 1!)

I need some diffrent opinions...

EDIT: I say yes now, thnx bobby!

Last edited by Smartiebell (2012-09-16 09:48:14)

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## #2 2012-09-16 08:47:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Who says that there is only only representation of the integer 1?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2012-09-16 08:54:46

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

There IS
1.0

01

1 1

2-1

x^0
etc...

I AM going both ways on this subject.
I'm just a little kid, don't confuse me too much!

Last edited by Smartiebell (2012-09-16 08:55:42)

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## #4 2012-09-16 08:58:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

How little?

In your post you admit or agree that

1 / 3 = .3333333...

So you are admitting that 1 / 3 has two representations, 1 / 3 and .33333333...
So why not 1?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #5 2012-09-16 09:11:42

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Agree.

Not 3rd grade little, but not College big.

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## #6 2012-09-16 09:13:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hmmm, there is alot of room in there.

To continue, no one argues that 3 pieces of a pie that is cut in thirds does not equal the whole pie do they?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #7 2012-09-16 09:20:22

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Yeah, I have never disagreed with that.
I know that 1 can be representated more than once, but what I am trying to figure out is if 0.999... written in standard form is the same as 1 written in standard form. Now I am 0.6 leaning toward Yes.But every so often my brain goes back to no.

And talking about brainpower, I am higher then 5th grade.

Last edited by Smartiebell (2012-09-16 09:21:38)

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## #8 2012-09-16 09:23:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Very good!

If 1 / 3 = .3333333... as we agree then we know that 3 of those 1 / 3's equals the whole thing or 1. Since

3 * .333333.... = .999999....

or

3 * .333333.... = 1

therefore you must agree that .999999.... = 1, it is just written differently. It is actually much easier to accept this one even if you can not follow it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #9 2012-09-16 09:30:51

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Thats what I wrote, right?!?!

And that means that 0.999... has the same properties as 1.
Like 50.999... = 5.
So we're sure about that, right?

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## #10 2012-09-16 09:32:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

This is not correct.

Like 50.999... = 5.

You have two decimal points in there.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #11 2012-09-16 09:35:56

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

What do you mean?

the period after the 5 is a sentence stopper period.

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## #12 2012-09-16 09:37:25

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Like (5 times 1= 5) and (5 times 0.999... = 5)

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## #13 2012-09-16 09:37:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Not the sentence stopper, this

50.999... we have an ellipsis on the end and two decimal points.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #14 2012-09-16 09:41:56

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

ok.
i thought  meant multiply.
So all that I had the problem with was the wording of the problem on the site. I say yes.

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## #15 2012-09-16 09:42:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Confusion gone? Are you okay with the idea?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #16 2012-09-16 09:44:43

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Yes. I just got a glimpse of (cue mystical music) The world of MAATH!

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## #17 2012-09-16 09:46:08

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Oh cool, I just turned into a Member!

sorry, off topic.

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## #18 2012-09-16 09:48:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Congratulations!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #19 2012-09-16 09:49:38

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Soo... let the people who have a problem with the idea cometh here! Cause I just figured it out, and I like to hear new ideas.

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## #20 2012-09-16 09:51:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Very few who come in here with that problem can ever come around to any new ideas.

Last edited by bobbym (2013-02-16 01:42:35)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #21 2013-01-29 23:18:06

john_gabriel
Member
Registered: 2013-01-29
Posts: 7

### Re: 1? Or not?

All the phony proofs in favour of 0.999... being equal to 1 are easily refuted:

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## #22 2013-01-29 23:29:08

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

### Re: 1? Or not?

I think that 0.999... = 1.

- n872yt3r
Math Is Fun Rocks!
By the power of the exponent, I square and cube you!

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## #23 2013-01-30 01:21:00

muxdemux
Member
Registered: 2012-12-23
Posts: 80

### Re: 1? Or not?

john_gabriel wrote:

All the phony proofs in favour of 0.999... being equal to 1 are easily refuted:

Interesting paper, John. Though I'll admit I'm skeptical.

In particular, on page 6 you prove that

by induction -- which does make sense to me. Where I start to have my doubts is where you show that

is absurd. Didn't you only prove

for the natural numbers?

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## #24 2013-01-30 01:30:53

bob bundy
Registered: 2010-06-20
Posts: 8,386

### Re: 1? Or not?

hi  john_gabriel

Welcome to the forum.

I read the article.  You wrote it?

One of the forum rules is:

"No Personal Attacks or Put-Downs. "

Hopefully the writer will understand that before contributing here.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #25 2013-01-30 02:08:06

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: 1? Or not?

Also a good point is that we should "ban" 0.999..., and similar numbers (that end with 9 recurring), because we would then have one representation in decimal notation for every number.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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The text passage contains a mathematical discussion and a question about whether 0.999... is equal to 1. The discussion includes a proof and various perspectives on the topic, but no definitive answer is provided within the text itself.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2012-09-16 08:10:51

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### 1? Or not?

My personal view- but I do not like the wording.

I (thought) it's like the "proof" of 1=2. There has to be a hidden mistake.

The problem( copied and pasted )
~~~~~~~~~~~~~~~~~
Let X = 0.999...
Then 10X = 9.999...

Subtract X from each side to give us:

9X = 9.999... - X

but we know that X is 0.999..., so:

9X = 9.999... - 0.999...
or: 9X = 9

Divide both sides by 9:

X = 1

But hang on a moment I thought we said X was equal to 0.999... ?

Yes, it does, but from our calculations X is also equal to 1. So:

X = 0.999... = 1

Therefore 0.999... = 1

~~~~~~~~~~~~~~~~~~

Common Sense: The integer 1 has a 1 in the ones place, and 0.999... has a zero.

But, (oh crack, I just got confused!)  1/3 = 0.333... and 1/3  3 =3/3=1, and 0.333...   3 =0.999...
so 0.999 would equal (1)! ( put parenthesis so not to be mistaken for 1!)

I need some diffrent opinions...

EDIT: I say yes now, thnx bobby!

Last edited by Smartiebell (2012-09-16 09:48:14)

Offline

## #2 2012-09-16 08:47:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Who says that there is only only representation of the integer 1?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #3 2012-09-16 08:54:46

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

There IS
1.0

01

1 1

2-1

x^0
etc...

I AM going both ways on this subject.
I'm just a little kid, don't confuse me too much!

Last edited by Smartiebell (2012-09-16 08:55:42)

Offline

## #4 2012-09-16 08:58:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

How little?

In your post you admit or agree that

1 / 3 = .3333333...

So you are admitting that 1 / 3 has two representations, 1 / 3 and .33333333...
So why not 1?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #5 2012-09-16 09:11:42

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Agree.

Not 3rd grade little, but not College big.

Offline

## #6 2012-09-16 09:13:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hmmm, there is alot of room in there.

To continue, no one argues that 3 pieces of a pie that is cut in thirds does not equal the whole pie do they?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #7 2012-09-16 09:20:22

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Yeah, I have never disagreed with that.
I know that 1 can be representated more than once, but what I am trying to figure out is if 0.999... written in standard form is the same as 1 written in standard form. Now I am 0.6 leaning toward Yes.But every so often my brain goes back to no.

And talking about brainpower, I am higher then 5th grade.

Last edited by Smartiebell (2012-09-16 09:21:38)

Offline

## #8 2012-09-16 09:23:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Very good!

If 1 / 3 = .3333333... as we agree then we know that 3 of those 1 / 3's equals the whole thing or 1. Since

3 * .333333.... = .999999....

or

3 * .333333.... = 1

therefore you must agree that .999999.... = 1, it is just written differently. It is actually much easier to accept this one even if you can not follow it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #9 2012-09-16 09:30:51

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Thats what I wrote, right?!?!

And that means that 0.999... has the same properties as 1.
Like 50.999... = 5.
So we're sure about that, right?

Offline

## #10 2012-09-16 09:32:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

This is not correct.

Like 50.999... = 5.

You have two decimal points in there.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #11 2012-09-16 09:35:56

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

What do you mean?

the period after the 5 is a sentence stopper period.

Offline

## #12 2012-09-16 09:37:25

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Like (5 times 1= 5) and (5 times 0.999... = 5)

Offline

## #13 2012-09-16 09:37:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Not the sentence stopper, this

50.999... we have an ellipsis on the end and two decimal points.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #14 2012-09-16 09:41:56

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

ok.
i thought  meant multiply.
So all that I had the problem with was the wording of the problem on the site. I say yes.

Offline

## #15 2012-09-16 09:42:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Hi;

Confusion gone? Are you okay with the idea?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #16 2012-09-16 09:44:43

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Yes. I just got a glimpse of (cue mystical music) The world of MAATH!

Offline

## #17 2012-09-16 09:46:08

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Oh cool, I just turned into a Member!

sorry, off topic.

Offline

## #18 2012-09-16 09:48:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Congratulations!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #19 2012-09-16 09:49:38

Smartiebell
Member
Registered: 2012-09-16
Posts: 16

### Re: 1? Or not?

Soo... let the people who have a problem with the idea cometh here! Cause I just figured it out, and I like to hear new ideas.

Offline

## #20 2012-09-16 09:51:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: 1? Or not?

Very few who come in here with that problem can ever come around to any new ideas.

Last edited by bobbym (2013-02-16 01:42:35)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #21 2013-01-29 23:18:06

john_gabriel
Member
Registered: 2013-01-29
Posts: 7

### Re: 1? Or not?

All the phony proofs in favour of 0.999... being equal to 1 are easily refuted:

Offline

## #22 2013-01-29 23:29:08

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

### Re: 1? Or not?

I think that 0.999... = 1.

- n872yt3r
Math Is Fun Rocks!
By the power of the exponent, I square and cube you!

Offline

## #23 2013-01-30 01:21:00

muxdemux
Member
Registered: 2012-12-23
Posts: 80

### Re: 1? Or not?

john_gabriel wrote:

All the phony proofs in favour of 0.999... being equal to 1 are easily refuted:

Interesting paper, John. Though I'll admit I'm skeptical.

In particular, on page 6 you prove that

by induction -- which does make sense to me. Where I start to have my doubts is where you show that

is absurd. Didn't you only prove

for the natural numbers?

Offline

## #24 2013-01-30 01:30:53

bob bundy
Registered: 2010-06-20
Posts: 8,386

### Re: 1? Or not?

hi  john_gabriel

Welcome to the forum.

I read the article.  You wrote it?

One of the forum rules is:

"No Personal Attacks or Put-Downs. "

Hopefully the writer will understand that before contributing here.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

## #25 2013-01-30 02:08:06

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: 1? Or not?

Also a good point is that we should "ban" 0.999..., and similar numbers (that end with 9 recurring), because we would then have one representation in decimal notation for every number.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline
user
The text passage contains a mathematical discussion and a question about whether 0.999... is equal to 1. The discussion includes a proof and various perspectives on the topic, but no definitive answer is provided within the text itself.

TYPE: SINGLE_QUESTION