Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: χ Χ ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -Ή ² ³ °

Login

Username

Password

Not registered yet?

#1 2012-09-17 06:10:51

Smartiebell
Member

Offline

0.999... = 1? Or not?

My personal view- up 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)! eek( put parenthesis so not to be mistaken for 1!)

swear
I need some diffrent opinions...

EDIT: I say yes now, thnx bobby!

Last edited by Smartiebell (2012-09-17 07:48:14)

 

#2 2012-09-17 06:47:42

bobbym
Administrator

Offline

Re: 0.999... = 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#3 2012-09-17 06:54:46

Smartiebell
Member

Offline

Re: 0.999... = 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 (2012-09-17 06:55:42)

 

#4 2012-09-17 06:58:19

bobbym
Administrator

Offline

Re: 0.999... = 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#5 2012-09-17 07:11:42

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

Agree.

Not 3rd grade little, but not College big.

 

#6 2012-09-17 07:13:05

bobbym
Administrator

Offline

Re: 0.999... = 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#7 2012-09-17 07:20:22

Smartiebell
Member

Offline

Re: 0.999... = 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 (2012-09-17 07:21:38)

 

#8 2012-09-17 07:23:40

bobbym
Administrator

Offline

Re: 0.999... = 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#9 2012-09-17 07:30:51

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

Thats what I wrote, right?!?!

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

 

#10 2012-09-17 07:32:32

bobbym
Administrator

Offline

Re: 0.999... = 1? Or not?

Hi;

This is not correct.

Like 5•0.999... = 5.

You have two decimal points in there.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#11 2012-09-17 07:35:56

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

What do you mean?

the period after the 5 is a sentence stopper period.

 

#12 2012-09-17 07:37:25

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

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

 

#13 2012-09-17 07:37:42

bobbym
Administrator

Offline

Re: 0.999... = 1? Or not?

Hi;

Not the sentence stopper, this

5•0.999... we have an ellipsis on the end and two decimal points.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#14 2012-09-17 07:41:56

Smartiebell
Member

Offline

Re: 0.999... = 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.

 

#15 2012-09-17 07:42:52

bobbym
Administrator

Offline

Re: 0.999... = 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#16 2012-09-17 07:44:43

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

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

 

#17 2012-09-17 07:46:08

Smartiebell
Member

Offline

Re: 0.999... = 1? Or not?

Oh cool, I just turned into a Member!

sorry, off topic.

 

#18 2012-09-17 07:48:10

bobbym
Administrator

Offline

Re: 0.999... = 1? Or not?

Congratulations!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#19 2012-09-17 07:49:38

Smartiebell
Member

Offline

Re: 0.999... = 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.

 

#20 2012-09-17 07:51:35

bobbym
Administrator

Offline

Re: 0.999... = 1? Or not?

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

Last edited by bobbym (2013-02-17 00:42:35)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#21 2013-01-30 22:18:06

john_gabriel
Novice

Offline

Re: 0.999... = 1? Or not?

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

 

#22 2013-01-30 22:29:08

n872yt3r
Power Member

Offline

Re: 0.999... = 1? Or not?

I think that 0.999... = 1.


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

#23 2013-01-31 00:21:00

muxdemux
Full Member

Offline

Re: 0.999... = 1? Or not?

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?

 

#24 2013-01-31 00:30:53

bob bundy
Moderator

Offline

Re: 0.999... = 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


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

#25 2013-01-31 01:08:06

anonimnystefy
Real Member

Online

Re: 0.999... = 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.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

Board footer

Powered by FluxBB