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Simple mathematical problem (?)

Colloden

Graduate Poster
Colloden
Joined
Oct 29, 2001
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There is an interesting maths question being posed on this Forum as the whether 0.999(recurring)=1

A suggested ‘proof’ is
X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=1

Hence 0.999(recurring)=1

I don’t like it at all. Although a number of different posters have come up with different suggestions, I am unconvinced that 0.999(recurring) is 1. Does anyone here know if there is a definite answer ?
 
Colloden said:
There is an interesting maths question being posed on this Forum as the whether 0.999(recurring)=1

A suggested ‘proof’ is
X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=1

Hence 0.999(recurring)=1

I don’t like it at all. Although a number of different posters have come up with different suggestions, I am unconvinced that 0.999(recurring) is 1. Does anyone here know if there is a definite answer ?
Click to expand...

No... 9X=9X, as far as I can tell. So X=9X/9, not 1.

My opinion only.
 
Or maybe you meant to say 9X=9.

Hmm. Something's wrong with that. Need to think about it more...
 
X=2
10X=20
10X-X=9X
9X=9X

hence 2=1 (or have I missed something)
 
Ah ha! 9X=8.999999999999999999999 (9*0.9999999)

In other words: 9X doesn't equal 9 (9.999-0.999), it equals 9X (9*0.999).
 
X=0.999(recurring)
10X=9.9999(recurring)



This is the step that seams questionble to me
 
Colloden said:
There is an interesting maths question being posed on this Forum as the whether 0.999(recurring)=1

A suggested ‘proof’ is
X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=1

Hence 0.999(recurring)=1

I don’t like it at all. Although a number of different posters have come up with different suggestions, I am unconvinced that 0.999(recurring) is 1. Does anyone here know if there is a definite answer ?
Click to expand...

It's a surreal number. But only if you decide to think of it in those terms. Not to be confused with the hyperreal numbers.
 
How can you state that X=1 when you just stated that X=.999?

I would say:

X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=0.999(recurring)


Your suggested proof is:

X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=1

But then...

X=1
10X <> 9.9999
Therefore X<>1
X=.999(recurring)


You can't just change 9X=9X to X=1 because it's really saying .999 = .999!!!
 
phildonnia said:
Would you accept that 0.9999.... is larger than any number less than 1?
Click to expand...

No, dammit, I wouldn't! It's a cover-up by mathematicians to hide the true assassins of John F Kennedy!
 
Mr Manifesto said:
Ah ha! 9X=8.999999999999999999999 (9*0.9999999)

In other words: 9X doesn't equal 9 (9.999-0.999), it equals 9X (9*0.999).
Click to expand...

hold it you are saying 0X=0.000(recurring)1
 
I don’t like it at all. Although a number of different posters have come up with different suggestions, I am unconvinced that 0.999(recurring) is 1. Does anyone here know if there is a definite answer ?
Click to expand...
Think of it this way:

What is the difference between 1 and 0.999(recurring)? The difference is infinitely close to 0, or in other words, the two are indistinguishable.

If 0.999(recurring) isn't 1 what on earth could it be? Is there a difference?
 
Earthborn said:
Think of it this way:

What is the difference between 1 and 0.999(recurring)? The difference is infinitely close to 0, or in other words, the two are indistinguishable.

If 0.999(recurring) isn't 1 what on earth could it be? Is there a difference?
Click to expand...

If you Square both numbers an infinet number of times on goes to 0 and the other goes to 1 therefore they are different numbers.
 
Earthborn said:
Think of it this way:

What is the difference between 1 and 0.999(recurring)? The difference is infinitely close to 0, or in other words, the two are indistinguishable.

If 0.999(recurring) isn't 1 what on earth could it be? Is there a difference?
Click to expand...

Of course. One is 1. The other is .999(recurring).

From a practical standpoint, they are the same. From a mathematical standpoint, they are unique values.
 
I think the proof you are looking for is:

X = 0.999(recurring)
10X = 9.999(recurring)
10X - X = 9X
But, by virtue of the first two equations, 10X - X also equals 9 (the recurring 0.999's cancel out)
So, since 10X - X = 9X and 10X - X = 9,
9X = 9
X = 1

We had a pretty long thread about this a few months back, I will try to find it.

But, any mathematician will tell you that 0.999(recurring) equals 1. He or she might throw in some mumbo jumbo about limits and whatnot, but for all intents and purposes, it's 1.
 
Earthborn said:
Think of it this way:

What is the difference between 1 and 0.999(recurring)? The difference is infinitely close to 0, or in other words, the two are indistinguishable.

If 0.999(recurring) isn't 1 what on earth could it be? Is there a difference?
Click to expand...

The difference is 1 infintesimel (which had better exist otherwise calculs has a serious problem)
 
boooeee said:
I think the proof you are looking for is:
Click to expand...

X = 0.999(recurring)
10X = 9.999(recurring)
10X - X = 9X
But, by virtue of the first two equations, 10X - X also equals 9 (the recurring 0.999's cancel out)
So, since 10X - X = 9X and 10X - X = 9,
9X = 9
X = 1

But 10X - X = 9X <> 10X - X = 9 unless X = 1
X <> 1
 
Here is a much better proof:

This assumes that you believe that 1/3 = .3333 (recurring)

1 = 3/3
= 3 * (1/3)
= 3 * .33333 (recurring)
= .999999 (recurring)


1 and .9999 (recurring) are the same number. They aren't close, they are the same.
 
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