NationStates Jolt Archive

I'm new to this fascinating game and would like to ask the community if the .999_ = (<>) 1 debate rips through this forum like a horrible whirlwind every few months. I know that on the other forums I visit it appears to rear its head based on some kind of horrible, underlying technological clock embedded in the forum script. If this plague does taint the waters here, I'm curious as to how bad its gotten. How many pages of worthless, uninformed "debate"? My masochism just needs satiating with all the gory details.

Yeah. Every so often it rears its ugly head, and 5 or 6 people go back and forth for 15 pages with long ass mathematical proofs as to why it does or doesn't work. It's amusing to read and very much over my head.

Well, you asked for it. If you define what the "..." means, then it should be clear. However, I'll produce the usual proof.

Between every pair of distinct real or rational numbers, there is an infinite amount of other numbers. There are no numbers between .999... and 1.

Well, you asked for it. If you define what the "..." means, then it should be clear. However, I'll produce the usual proof.

Between every pair of distinct real or rational numbers, there is an infinite amount of other numbers. There are no numbers between .999... and 1.I'm fairly confident that no one "asked for it".

EDIT: Blah, I guess Sdaeriji's post could be construed as "asking for it". I rescind my statement.

Well, you asked for it. If you define what the "..." means, then it should be clear. However, I'll produce the usual proof.

Between every pair of distinct real or rational numbers, there is an infinite amount of other numbers. There are no numbers between .999... and 1.
What the hell is the "..." then?

Let's see...1/9 = .111111111111...

3/9 = .33333333333...

9/9 = .99999999999...

1/1 = 1

3/3 = 1

9/9 = 1

1 = .99999999999...

What the hell is the "..." then?
"repeating"

I'm fairly confident that no one "asked for it".
Well, you got it anyway. Look what you've started.

To answer your original question, I haven't been here long enough to know. I'm rather shocked to see any math questions, though. Of course, I'm an administrator at a math forum, and I guess we do get the occasional religion thread. The worst ones, though, are the proofs that 1=2. Questions about 0^0 get old as well.

What the hell is the "..." then?
The ... is taking the limit as the number of decimal places used goes to infinity.

The ... is taking the limit as the number of decimal places used goes to infinity.
Hmm...
I say that, since "infinity" isn't a specific number, the case can't truly happen that you can reach an end, and you must stop before you can even get to the point where you can say that there is nothnig between them.

Then again, I'm no math expert.

Well, you got it anyway. Look what you've started.

To answer your original question, I haven't been here long enough to know. I'm rather shocked to see any math questions, though. Of course, I'm an administrator at a math forum, and I guess we do get the occasional religion thread. The worst ones, though, are the proofs that 1=2. Questions about 0^0 get old as well.
I love the proofs that "1=2"!
The one the the divide by zero error is the best. A friend of mine wouldn't believe me until I gave him a calculator so he could work through it.
:D

Hmm...
I say that, since "infinity" isn't a specific number, the case can't truly happen that you can reach an end, and you must stop before you can even get to the point where you can say that there is nothnig between them.

Then again, I'm no math expert.
Limits never actually involve the number in question. For limits to infinity, you just say that it's greater than any number you can specify.

Meh ... it really depends on if you think of math in terms of abstracts or absolutes.

If you think of it in terms of absolutes (like an Algebra or Calculus junkie), then you will never agree that 0.999... == 1.000...

However, if you think like an Astronomer or Geometrist, then you'd know that if you had 1 cow and chopped off 0.000000000000000000000000000000001 of it, then you'd still have 1 whole cow.

If you take mathematics to its musical level, then based off the human ear, then 0.8 and 1.2 may as well be exact.

Funny thing, math. When you study it enough, you begin to realize that it's like the Bible or the 2nd Amendment ... the more you argue it, the dumber you are.

The ... is taking the limit as the number of decimal places used goes to infinity.
Fascinating. Defining "..." that way makes it impossible for anyone who knows what's going on to deny that .999... = 1. I always just interpreted "_" "..." or whatever else as "repeating", which is the issue about which people care, not whether the limit equals one. But then, it's a cardinal sin to manipulate representations using infinity without using limits, isn't it?

So, do I have the ability to delete threads that I post? In case people actually start debating this instead of just musing and comparing interpretations.

So, do I have the ability to delete threads that I post? In case people actually start debating this instead of just musing and comparing interpretations.
You can't delete it, but you can ask a mod to lock it.

If you think of it in terms of absolutes (like an Algebra or Calculus junkie), then you will never agree that 0.999... == 1.000...
I quite disagree. The whole point is that they are "absolutely" the same. No one has a problem with the fact that they're essentially and practically the same. It bothers people that they are merely different representations of the exact same number.

EDIT: Aw, hell, I have gone and done it. Now I'm starting to debate. May the Good Lord have mercy on my repentant soul. Sooooo . . . how would I go about asking a mod to lock it? (Had I known I couldn't delete my thread, I likely wouldn't have posted this. I knew I was asking for trouble, but I thought I'd be able to quickly engage in damage control.)

it's a cardinal sin to manipulate representations using infinity without using limits, isn't it?
Bingo. I don't think you can delete the post.

Which is why the famous proof that goes something like this (albeit more smoothly done, because this is from memory):

x = .999_

10x = 9.999_

10x - x = 9x

9.999_ - .999_ = 9 = 9x

9x/9 = x

9/9 = 1

.999_ = 1

May be interesting and good at duping people that don't know better, but it's mathematically faulty because you're playing with infinity like it's just another one of the boys.

EDIT: Aw, hell, I have gone and done it. Now I'm starting to debate. May the Good Lord have mercy on my repentant soul. Sooooo . . . how would I go about asking a mod to lock it? (Had I known I couldn't delete my thread, I likely wouldn't have posted this. I knew I was asking for trouble, but I thought I'd be able to quickly engage in damage control.)
You'd go to the moderation forum:
http://forums2.jolt.co.uk/forumdisplay.php?f=1231

And post about it.

For now, I'll hold my breath and hope no one else jumps in on this and makes a fool out of me and my naive line of questioning.