Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

Agree.

Not 3rd grade little, but not College big.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

What do you mean?

the period after the 5 is a sentence stopper period.

Offline

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

Offline

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

Oh cool, I just turned into a Member!

sorry, off topic.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

Congratulations!

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

**Online**

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,092

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.**

**Online**

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

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

thenewcalculus.weebly.com/uploads/5/6/7/4/5674177/proof_that_0.999_not_equal_1.pdf

Offline

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

I think that 0.999... = 1.

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

Offline

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

john_gabriel wrote:

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

thenewcalculus.weebly.com/uploads/5/6/7/4/5674177/proof_that_0.999_not_equal_1.pdf

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

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,268

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

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,954

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