[ekudamram]

I posted on facebook;

' 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

[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.

[Dirac Delta Function]

He can always end this argument with "well I'm shagging your sister".


Seriously, just leave it.

[Cephalus]

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.

[Cephalus]

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.

[Cerdog]

(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?

[tazmaniac97]

Why would you bother. And besides how am I supposed to know, I don't even have any GCSEs,

[Manitude]

(Original post by Cerdog)
You called?

Bravo, sir. Just the person I was looking for.

[Cerdog]

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:

[TenOfThem]

OP

Your let x= method is fine


Your sister could do better for herself

[nuodai]

I'm going to close this thread before the usual 0.999...=1 'debate' starts; I hope this is okay but I think your question has been answered.

You could always show him this video:


For more verification:
http://www.thestudentroom.co.uk/showthread.php?t=188551
http://www.thestudentroom.co.uk/showthread.php?t=329646
http://www.thestudentroom.co.uk/showthread.php?t=660604
http://www.thestudentroom.co.uk/show....php?t=1285322
http://www.thestudentroom.co.uk/show....php?t=1348503
http://www.thestudentroom.co.uk/show....php?t=1655202
http://www.thestudentroom.co.uk/show....php?t=1927251