.999.... (Repeating) is equal to one?

When you say something like "0.999 repeating", you're saying "the limit as 'pattern X' approaches infinity."

edited 9th Sep '11 10:27:55 PM by Clarste

Wait a minute. So pi isn't a number either? Real numbers have infinite "accuracy", or exactness, so I don't see what's wrong with having infinite 9's.

It's true that "as the number of nines approaches infinity, the value of .9999 etc. approaches one." But that should not be taken in as a rounding concept. It's only "close to 1" when we deal with "many 9's". We ultimately want to deal with infinite 9's - this is where limits come in.

edited 9th Sep '11 10:38:10 PM by abstractematics

I have to ask... does anyone really care about this who isn't a paid mathematician or scientist...?

Well the topic asked for it. This thread deals in the scope of mathematics, so there's no "basically equal" here. Either they're same or they're not.

edited 9th Sep '11 10:32:39 PM by abstractematics

My question is, is there a functional difference?

Theoretically, .999... is 3/3, or... 1. So, I repeat, would it matter to anyone besides those for whom this is a career?

That was never the point of this thread.

"It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know." - Titchmarsh, E. C.

So, this thread has .999 repeating problems, but equaling 1 ain't one?

Infinity isn't a number in the usual sense, but mathematicians work directly with infinite objects, collections, quantities, and processes all the time. It can be hard to grasp if you don't know the mathematics behind it, but there's no problem at all with having, say, a number which is represented by an infinite string of digits. Of course, you can't physically write all of them, but you don't need to, since you can write notation that expresses the same thing.

More concisely, there is indeed an actual number represented by 0.999... — yes, with an infinite number of nines — and that number is more commonly represented by the symbol '1'.

edited 9th Sep '11 10:39:12 PM by Enthryn

People really care because it challenges their fundamental beliefs about the world. So basically it matters as much to a layman as theological arguments do.

Also, I don't think it matters much to scientists either, practically speaking. I'm reasonably sure we don't have any instruments capable of taking measurements up to infinite significant digits yet.

edited 9th Sep '11 10:41:46 PM by Clarste

Knowing that pi is an irrational number is useful... for high schoolers. Unless your career involves advanced math (and/or circle measurement...), though, you won't give a damn after high school and college...

If.

oh man oh man oh man I just got to use a Spartan one-liner on a math problem! I ARE ULTRAGEEK

edited 9th Sep '11 10:39:39 PM by BlackHumor

The OP asked if .9_ equals 1 or not. It's number theory and mathematical analysis. Whether it's "practical" is not the point here.

Well, I guess I have my answer: only the math nerds care...

knowing digits of pi are kinda useless in and of itself. A really small amount of digits, less than 50, I think, is enough to calculate the circumference of the universe down to the width of an H atom.

[1]

Isn't the universe effectively infinite through perpetual expansion...?

Furthermore, who the fuck would want to know how big the universe is? We'll never see a percent of a percent of a percent of it, even...

Why did you post here if you don't care? Sure, in the real world, it doesn't matter if .9_ is exactly 1 or not. Many simple applications of math in the real world tend to deal with finite quantities anyway, and approximatins are widely used.

But in a formal mathematical context, it's a matter of whether this number is 1, a fundamental unit, or just some random meaningless decimal. That's what the OP asked and that's what we're answering.

Even if we were to extrapolate out to the heat death of the universe, beyond which point we'd have all kinds of reasons to no longer give an ass, we still wouldn't need a whole lot of digits.

edited 9th Sep '11 10:47:12 PM by Pykrete

Because I do not comprehend the mindset it would take to make someone care about such an insignificant thing when there are so many more important issues to deal with...

If mathematics and abstraction are not your taste, you don't have to post here. Like I said, 1 is pretty important in mathematics.

I'm asking you to explain. No need to be pretentiously hostile because you grasp the math easier than I do. That would be why many people have an immediate and intense hatred for math: those who are good at it do not stop to explain their genius to the rest of us...

Mathematics is of near-universal importance in the sciences. It's important within mathematics for such fundamental matters to be fully understood, even when they're too abstract to have immediate practical applications.

...that didn't really tell me anything. It just restated the "it's important to us because we say so" idea...

Because it's cool? Why not? What properties make anything else more worth thinking about?

Well what do you want us to explain to you? This topic is purely about mathematical truth, where someone asked a simple question about numbers. It's like when someone posts a math help topic or wants to talk about particular theorems.

edited 9th Sep '11 10:59:19 PM by abstractematics