I just punched it into a calculator. Was that right?
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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?
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.
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.
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. :wink:
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. :wink:
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.
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.
You can't prove a paradox.Quote:
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.
No, no and no. Numbers don't exist they are just mathematical objects not physical objects.Quote:
Math is logic related to numbers. Numbers exist, we didn't create them. They, and thier laws, just are.
Actually mathematician can.Quote:
I suppose that your right, human minds can't comprehend infinity.
Maths is a language, it is not physical.Quote:
But that doesn't mean that there is a paradox, or that math laws are any less true than the existance of gravity.
What?
A thing does not have to be physical to exist.
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.
I think that you're just trying to play devil's advocate...Quote:
Actually mathematician can.
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.