Thread: Does 0.9 repeated = 1?

I don't think you can use standard operations on transcendentals to get a rational (save pi/pi etcetera). In decimal form it's actually 19.99909997918947.

Find the Fourier series representation of f(x)=1.

Yeah I'll get back to you on that one this time next year maybe.

The only thing I know about Fourier Series is that they represent functions by sums of trig functions. So I guess sin^2x + cos^2x is involved. But I really have no idea.

Why?

Originally Posted by Xei

Yeah I'll get back to you on that one this time next year maybe.

The only thing I know about Fourier Series is that they represent functions by sums of trig functions. So I guess sin^2x + cos^2x is involved. But I really have no idea.

Why?

It's just that making the Fourier series of 1 will be tedious and the answer will always look ugly no matter how many terms you keep.

Ok, try the Fourier series of (sin x)^3

I'm still in school. Honest.

No. It goes: 0.9, 1.8, 2.7, 3.6, 4.5. Or, 0.90.90.9. That doesn't look like 1 either.

Originally Posted by Venomblood

No. It goes: 0.9, 1.8, 2.7, 3.6, 4.5. Or, 0.90.90.9. That doesn't look like 1 either.

EDIT: oh.

I think he's trying to be sarcastic...

1 equals 1 = equals 1 == 1 === 1

One is one is one. That's it. It'd not one because there's no such thing as a number infinitely close to .999 repeat. It's either 1 or 0 %. Anything thing lower would be one, anything higher would be 0. 1 + 0 = 0 =10 +1 +5 +2 + 0 = 8972566, which then equals nothing at a all. A sorry satanic fagot without a phone number, Adrian Peterson, which is me.

Huh? At any rate, your right. And since one equals one, (1=1,) then .9 repeating equals one, (.9~=1,) which is just another way to say 1=1.

Originally Posted by spockman

then .9 repeating equals one, (.9~=1,) which is just another way to say 1=1.

You proved that it does, and mathematics says that it does, but how does it?

Originally Posted by Universal Mind

You proved that it does, and mathematics says that it does, but how does it?

0.9~ is clearly the short form of the geometric series 9/10 + 9/100+ 9/1000, and so on.

Let S = 0.9~ = 9/10 + 9/100 + 9/1000 + ...
then S/10 = 9/100 + 9/1000 + 9/10000 + ... = S - 9/10

so S/10 = S - 9/10
so S = 10S - 9
9S = 9
S=1

That was the most basic, constructivist proof I can possibly think of. If you still don't understand, then you're just beyond hope.

Originally Posted by drewmandan

0.9~ is clearly the short form of the geometric series 9/10 + 9/100+ 9/1000, and so on.

Let S = 0.9~ = 9/10 + 9/100 + 9/1000 + ...
then S/10 = 9/100 + 9/1000 + 9/10000 + ... = S - 9/10

so S/10 = S - 9/10
so S = 10S - 9
9S = 9
S=1

That was the most basic, constructivist proof I can possibly think of. If you still don't understand, then you're just beyond hope.

I think you need to read all of a post before acting like an 8th grader about it next time. Read my last post, and you might catch the irrelevance of your post. Give it a whirl and see if you can catch what I am talking about.

Give up? I said it has been proven that 0.999... = 1 but that it has not been explained how it is. Your proof, like Spockman's, proved that the two figures are equal. I am not asking for proof that they are equal. I am asking how an infinite repetition of 9's following 0 and a decimal can equal 1. Do the 9's go on forever, or do they not? Obviously a paradox is involved. Proving the truth of the paradox is not the same as explaining the resolution of the paradox, and saying that branches of mathematics say that the paradox is true is not the same as explaining the resolution of the paradox. If you still don't understand what I am asking, then you are beyond hope.

Originally Posted by Universal Mind

I think you need to read all of a post before acting like an 8th grader about it next time. Read my last post, and you might catch the irrelevance of your post. Give it a whirl and see if you can catch what I am talking about.

Give up? I said it has been proven that 0.999... = 1 but that it has not been explained how it is. Your proof, like Spockman's, proved that the two figures are equal. I am not asking for proof that they are equal. I am asking how an infinite repetition of 9's following 0 and a decimal can equal 1. Do the 9's go on forever, or do they not? Obviously a paradox is involved. Proving the truth of the paradox is not the same as explaining the resolution of the paradox, and saying that branches of mathematics say that the paradox is true is not the same as explaining the resolution of the paradox. If you still don't understand what I am asking, then you are beyond hope.

I said it has been proven that 2/4 = 1/2 but that it has not been explained how it is. Your proof, like Spockman's, proved that the two figures are equal. I am not asking for proof that they are equal. I am asking how 2 divided by 4 can equal 1 divided by 2. Does the 2 go into the 4, or does it not? Obviously a paradox is involved. Proving the truth of the paradox is not the same as explaining the resolution of the paradox, and saying that branches of mathematics say that the paradox is true is not the same as explaining the resolution of the paradox. If you still don't understand what I am asking, then you are beyond hope.

Conceptionally at how we see the world .9999999999 is one whole even though logic tells us otherwise. I don't believe human thought can be defined with logical math, it's more abstract than anything else.

Originally Posted by drewmandan

I said it has been proven that 2/4 = 1/2 but that it has not been explained how it is. Your proof, like Spockman's, proved that the two figures are equal. I am not asking for proof that they are equal. I am asking how 2 divided by 4 can equal 1 divided by 2. Does the 2 go into the 4, or does it not? Obviously a paradox is involved. Proving the truth of the paradox is not the same as explaining the resolution of the paradox, and saying that branches of mathematics say that the paradox is true is not the same as explaining the resolution of the paradox. If you still don't understand what I am asking, then you are beyond hope.

How is the fact that 2/4 = 1/2 a paradox? The 2 does go into the 4 without seemingly contradicting anything. Is that the best you've got?

Math is logic related to numbers. Numbers exist, we didn't create them. They, and thier laws, just are. The laws of physics just are as well. We can play the why game all day. But that game can be applied to any fact. Example, physics. The law of gravity can be attributed to another law which can be attributed to another law and so on and so forth, but eventually the resoluteness of it just has to be accepted, as a point is reached where we run out of explanations and have to resort to seemingly circular logic. I suppose that your right, human minds can't comprehend infinity. But that doesn't mean that there is a paradox, or that math laws are any less true than the existance of gravity.

Proving the truth of the paradox is not the same as explaining the resolution of the paradox, and saying that branches of mathematics say that the paradox is true is not the same as explaining the resolution of the paradox.

You can't prove a paradox.

Math is logic related to numbers. Numbers exist, we didn't create them. They, and thier laws, just are.

No, no and no. Numbers don't exist they are just mathematical objects not physical objects.

I suppose that your right, human minds can't comprehend infinity.

Actually mathematician can.

But that doesn't mean that there is a paradox, or that math laws are any less true than the existance of gravity.

Maths is a language, it is not physical.

Originally Posted by Universal Mind

How is the fact that 2/4 = 1/2 a paradox?

How is the sum of a geometric series a paradox?

Originally Posted by wendylove

You can't prove a paradox.

What?

Originally Posted by wendylove

No, no and no. Numbers don't exist they are just mathematical objects not physical objects.

A thing does not have to be physical to exist.

Originally Posted by drewmandan

How is the sum of a geometric series a paradox?

Do the 9's go on forever, or do they end? If they go on forever, then how do they stop at 1? If they end, how many 9's are in there?

Saying that math says the two figures are equal does not answer the question. The two figures are apparently equal, but that does not create an answer to what I am asking. It creates a paradox. The paradox has not been resolved. It has only been proven to be a real paradox.

Originally Posted by Universal Mind

Do the 9's go on forever, or do they end? If they go on forever, then how do they stop at 1? If they end, how many 9's are in there?

There is an infinite number of 9's.

Actually mathematician can.

I think that you're just trying to play devil's advocate...

Originally Posted by drewmandan

There is an infinite number of 9's.

I agree, but...

Then how is 1 ever reached?

Remember that I am looking into the nature of converging geometric series, so the mere explanation that a converging geometric series is involved is not enough. I am trying to dissect that principle.

The proof of convergence of geometric series involves analysis and is DEFINITELY too advanced for you to understand.

It involves proving that the partial sums are Cauchy.