Then STFU. Seriously.

Did you guys solve this yet?

Free IS right, despite the fact that he's being very angry about it

Spoken with the logic of a true Christian!

Okay, mathematics is based on proofs, right? Here's the simplest proof I can think of, in completeness. If you want to refute that 0.9r = 1, you have to find a flaw in this proof.

It is simple.

1/9 = 0.1111111......

9* 0.111111111... = 0.999999999...

9* 1/9 = 9/9 = 1

.99999999... = 1

Along the same lines, 2 + 2 = 5, for very large values of 2.

But 1/9 != 0.1111111

It`s same case of approximation. 0.1(1) converges to 1/9, but is forever smaller, then it is.

READ MY PROOF.

Divide 1 by 9 by hand using long division. You will get a repeating pattern of 1s. Keep doing the division until the 1s stop repeating.

But they never stop repeating, that`s the problem.

Therefore, 1/9 will be always bigger, then 0.1(1). There will be always some remainder, no matter, how long you will be dividing.

No. 1/9 is exactly equal to a zero and a decimal point followed by a neverending string of 1s. That is what the result of the division shows. It sounds impossible, but that's what it is. There is no approximation.

Infinite is key here. It infinitely converges to 1/9.

But it`s not equal. Sorry, but such is math.

Even at the infinite point down the division, there`s always remainder. Nothing you can do with it. It gets smaller and smaller, but never becomes zero.

Thus, in terms of mathematical analysis, 0.1(1) CONVERGES to 1/9.

______________________________________________________________

However, just to be clear here... In the day-to-day calculations, assuming that 1/9=0.11 is mostly acceptable. Noone needs infinite precision on shopping trip.

Look, I'm not even talking about a series anymore. I'm not adding together a sequence of 0.0(n)9s. All I'm doing is dividing 1 by 3 and seeing what comes out. And what comes out is a neverending string of 3s. Hell, I'll do it with 1 divided by 1!

Now, each time I add another 9 I get closer to 1, but I will not be done with the division problem. I will only be done with the division problem when there are an infinite number of 9s. In real life I can't possible do that because I don't have enough space or time. But we can say that 1 is equal to the result of that division problem, which is...?

We can`t say, that it`s EQUAL. We can say, that it converges, and CAN be taken as equal for most of calculations.

But formally, it`s not equal, even though for all the practical purposes of someone not employed at math college, it acts as it`s equal.

Once again - it is SAFE to ASSUME it IS. It is not, but the difference is SO insignificant for most purposes, that it can be ignored.

Holy crap, this is pointless! But if I give up arguing now you'll think you've won, when really your ignoring everything I say!

You can't use the word convergence when we're not talking about series!

But irrational numbers ARE series. You can`t represent them any other way, if you want to compare them to anything.

Here's the problem, in the set of rational numbers 0.9... equals 1. This is mathematical fact, to argue otherwise demonstrates a clear misunderstanding of at least one mathematical idea.

Find this idea that you're getting wrong and get it right, because apparantly other people can't persuade you of anything even when they're right. During the course of this thread I looked at some sources and for a while I was a little uncertain about the answer, but then I kept looking and was sure of it.

Why don't you try doubting your assumptions for a change?

But 0.9(9) is NOT a rational number. It`s irrational.

But it can be represented as a fraction: 1/9.

It's rational. If you want to argue that it is irrational, pull out a proof.

No, pi is an irrational number. 0.99 repeating is not. at all. ever.

Also, I meant to say real numbers. The only reason I didn't edit is because it's already been referred to.

Look...

0.9(9) can not be equalised like a normal number. You`re equaling infinite series sum to certain number. That`s why term "converges" was coined.

0.9(9) can not be treated like a rational number, simple as that. If you want to treat it as rational number, well, then:

1) It has to be finite.

2) It CAN be approximated to 1 for calculations.

But as long as you keep claiming, that 0.9(9) in infinite form should be compared to 1, you`re asking - "Lightrbulb or parrot?"

stop posting here

no you don't understand limits even though you try to use calculus terms

yes it can be treated as a rational number becaue it is one.

What? No it doesn't. The textbook definition of a rational number is any number that can be expressed with a fraction. (1/3) is a repeating decimal but it's still a rational number. :downs:

It can because the fraction for 0.999 repeating is 1/1. Because 0.999 repeating is equal to 1.

lurk more

In addition to what Jon said, an irrational number is both non-terminating (like 0.9...) and non-repeating. The reason we don't know the zillionth digit of pi is because it never repeats. If it repeated every hundred digits it would be rather easy to work out.

Did you know that the 5,343,343,235,214,111th digit of 0.9... is 9? I knew that, because it's RATIONAL.

Here's a new fact. You are not as good at mathematics as you think you are.

We have a contradiction here.

You claim, that 0.9(9) can be represented as fraction.

While I claim, that it`s a sum of infinite series, and therefore, could only be converging to such.

_______________________________________

Frankly, this is not a mathematical problem, anymore. It`s semantics and terminology.

Russian univesrsities always set aside converging and equaling, for purposes of keeping mathematics disambiguated.
I suppose, that USA universities prefer not to overload students with extra terminology, instead.

At this point, the argument is not as much "this is correct, and this is not", as over the way of describing the fact.

I have to conclude, that this point is just represented differently in different schools of mathematics.. And therefore, as useless, as previous argument about comas.

There is no inherent fallacy within each method - one is designed for simplifying, while other - for pinpoint accuracy. I imagine, that both have their own applications and merits.

Feel free to stick to your method, I stick to mine.

On this note, I withdraw from the argument, as it deteriorates into petty squabble... Which, I`ve already fullfilled my monthly norm of.

You know, I don't believe that stuff about Russian universities at all. I know they teach math a bit differently over there, but this seems like too big a disagreement to be split over.

Alice Shade declares internet victory.

Actual winners: the rest of us

Ok, fine, let's do the problem as a sum of infinite series.

.999999... = 9(1/10) + 9(1/10)^2 + 9(1/10)^3 + ....9(1/10)^n ; n => infinity.

By the convergence theorem, this converges to ar/(1-r) = 9*(1/10) / (1-(1/10))

= (9/10) / (9/10) = 1

It still works.

http://ru.wikipedia.org/wiki/0.999...

EDIT: Nevermind. Just click the link.

I challenge you to find a single source to back that up. Just one.

Wolfram says you're full of crap on all counts. Are we to believe that the makers of Mathematica don't understand rational/irrational numbers?

No, actually, you withdraw because you don't have any proof and you don't understand the basic definition of irrational numbers, something my 12 year old brother understands better than you.

Thus, you attempt to "take the high road" by claiming this argument about why you are totally wrong is just a squabble, when in reality it's just a massive bashing of how little you understand about math.

In other words, he pulled a Friend14?

I can't believe I missed this!

0.9 recurring is exactly equal to 1.

I've even managed to get Izzy to understand this simple concept and by her own admission she's terrible at maths :downs:

Who cares? You get the same damn answer, unless you're using floating point math.

Incidentally, 1/3 == 0.1 (in base 3). Base 10 is boring. Do your math in something else, like base 7.

And whoever that was dividing 1 by 1 and getting 0.999... - that's stupid. Any first grader would tell you that 1 divided by 1 is 1. You don't need to do stupid mathematical theatrics with something this trivial.

Also, the difference between 0.999.. and 1 is 1/infinity. Duh. And I don't care if you blather on about 1/infinity just being zero, who cares?

For someone who doesn't care that's a lot of text.

Sometimes it's easier to get mathematical concepts across to people who recognize they're bad at math than to people who don't.

I'm willing to believe he actually is Friend14.

You're quite right there sir.

I was wondering about this myself. In the Monty Hall thread, I couldn't help thinking that this was exactly what would happen if Friend14 decided he knew statistics.

Friend14 is to Physics as Alice is to Logic

Alice, seriously, shut up and go away.