## A Conversation for Logical Completeness

### something sort of interesting

Wayfarer -MadForumArtist, Keeper of bad puns, Greeblet with Goo beret, Tangential One Started conversation Jan 23, 2001

there is no fraction for .9 repeating (that's .9999999999999999999999999999999999999999....... and so on forever)

### something sort of interesting

Decaf Silicon Posted Jan 24, 2001

Our math class keeps that as a running joke, as we've been told that .9 repeating = 1, through some formula, since it's 9/9. (5/9=.55555..., etc)

In a way, it does equal 1, as it's infinitely near 1.

-- Dmitri

### something sort of interesting

HenryS Posted Jan 24, 2001

I *does* equal one.

To prove it properly, you need to write 0.999999... as an infinite sum of the form:

Sum(n=1 to oo) { 9*(10)^(-n) }

then show that this sum converges to 1. But you need first year undergraduate mathematics to do that.

### something sort of interesting

Wayfarer -MadForumArtist, Keeper of bad puns, Greeblet with Goo beret, Tangential One Posted Jan 24, 2001

really? you do? i have used that formula in class before, but i wasn't a graduate anything then. it is near enough to one as makes no difference, but it isn't, quite. i think its 1-(.000......1(zero repeating with a one after all the zeros which is as close as you can get to zero and still not be))

### something sort of interesting

HenryS Posted Jan 25, 2001

Well, you need the university maths to define precisely what 'converges' means. Intuitively yes, it keeps getting nearer to 1, but thats not enough to be sure.

"1-(.000......1(zero repeating with a one after all the zeros which is as close as you can get to zero and still not be))"

This isnt a number. There is no place to put that one after all the zeros, because the zeros never end.

### something sort of interesting

DMarsh3000 Posted May 31, 2001

x = 0.99999...

10x = 9.99999...

Subtracting equations, 9x = 9

So x = 1, that is, 0.9999... = 1.

DM

### something sort of interesting

Researcher 178849 Posted Jun 3, 2001

This discussion lacks a definition of what is meant by writing 0.999... One cannot just use symbols arbitarily.

### something sort of interesting

HenryS Posted Jun 10, 2001

I'm assuming 0.999,,,, means:

sum from i = 1 to infinity of 9/(10^i)

With that definition its possible to show this sum converges to 1.

Key: Complain about this post

### something sort of interesting

- 1: Wayfarer -MadForumArtist, Keeper of bad puns, Greeblet with Goo beret, Tangential One (Jan 23, 2001)
- 2: Decaf Silicon (Jan 24, 2001)
- 3: HenryS (Jan 24, 2001)
- 4: Wayfarer -MadForumArtist, Keeper of bad puns, Greeblet with Goo beret, Tangential One (Jan 24, 2001)
- 5: HenryS (Jan 25, 2001)
- 6: DMarsh3000 (May 31, 2001)
- 7: Researcher 178849 (Jun 3, 2001)
- 8: HenryS (Jun 10, 2001)

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