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1. Can someone please explain why this is true?

' Q: How many mathematicians does it take to change a lightbulb?'

A: 0.999...'

An argument then ensued between me and my sisters boyfriend (not a maths person, but still when I explained it he just didn't accept it)

My explanations (albeit crudely done) were thus:

Let x = 0.999...
10x = 9.999...
9x = 10x - x
9x = 9.999... - 0.999...
9x = 9
x = 1

or

If 1/9 = 0.111...
1/9 * 9 = 1
therefore 0.111... * 9 = 0.999... = 1

Can anyone give me another way of explaining this, or even something which could help me understand it more?

Cheers
2. Re: Can someone please explain why this is true?
Someone has a nice proof in their sig on TSR actually. You'll need to understand the notation but it's not too hard.
3. Re: Can someone please explain why this is true?
He can always end this argument with "well I'm shagging your sister".

Seriously, just leave it.
4. Re: Can someone please explain why this is true?
Another way is to write 0.999999 as a geometric progression ie

0.9 + 0.09 + ...

then find the sum to infinity.

Or you could explain it using the Dedekind Cut way.
5. Re: Can someone please explain why this is true?
A more rudimentary way to 'prove' that they are the same would be to first assume they are distinct, then try and find a number that lies between the two.

As this will fail, we conclude they must be the same same.
6. Re: Can someone please explain why this is true?
(Original post by Manitude)
Someone has a nice proof in their sig on TSR actually. You'll need to understand the notation but it's not too hard.
You called?
7. Re: Can someone please explain why this is true?
Why would you bother. And besides how am I supposed to know, I don't even have any GCSEs,
8. Re: Can someone please explain why this is true?
(Original post by Cerdog)
You called?
Bravo, sir. Just the person I was looking for.
9. Re: Can someone please explain why this is true?
Actually, just on the off chance I decide to change my signature and someone reading this thread in the future is confused, here is the proof in picture form:

10. Re: Can someone please explain why this is true?
OP

Your let x= method is fine

Your sister could do better for herself
11. Re: Can someone please explain why this is true?
Last edited by nuodai; 05-08-2012 at 11:16.