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Author | Topic: A question of numbers (one for the maths fans) | |||||||||||||||||||||||||||
riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Looking at the graph at the bottom of the first link, is always how I had pictured .999... in my mind. That is how I can conceive .999... becoming 1. The resolution of the infinite 9's becomes so small that it becomes 1.
My question is, why does .999... become 1, and .333... never be anything more that .333... ? Or how about this. In the equation 2+1-1=2 You can reverse the last 2 calculations, and still get the same answer2-1+1=2, but here you can't: ∞ + 1 - ∞ = 0 ∞ - ∞ + 1 = 1
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Yes, I took algebra, but rarely have to use it. So it is very rusty.
That's about as far as I got, as I had a rough childhood, and had to drop out and start working. So I do appreciate everything, that everyone is saying to me here. It's not like I don't think about mathematical concept's all the time. It is my favorite subject. I use math immensely in my work, and my hobbies, but not at calculus levels. I have been thinking lately of going to college, to get an engineering degree, it's never too late. I invented parts of trigonometry out of necessity, because I am a master sheet metal layout mechanic. At one time, I needed to figure out what the other sides, and angles of a triangle would be, if I only knew one angle, and one length. I had invented some formulas, but I can't seem to find them. I later learned that it was similar to sin, and cos. Sheet metal fabrication is all about triangulation, and after doing for so many years, you gain a different perspective on the world. There is nothing I couldn't break down into a 2D pattern. I could cover you in metal. Now, about the formula. If that formula works for 10x, shouldn't it work for 2x? also shouldn't the result be similar when we use .333...? Why does .999... resolve to a 1, and .333... never resolve?
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
In 0.999 we don't lose the 9/1000. All that happens is that the 1000ths column becomes 0 because the digits are shifted up one column (in base 10). when there are an infinite number of 9s we don't put a zero at the end, but the essential operation (shifting the digits up a column) can still happen. This is part and parcel of the number system. In wikipedia, what I am saying is considered wrong, but worthy of mention.
quote: Repeating decimal - Wikipedia If we can't add a 0 to the end, then 2*.999... = 1.999... ?And if so used in your equation, x still equals 1? Even though 2*.999 = 1.998You don't find a problem with this? Shouldn't infinity and time be directly related to one another?Could it be, that at the moment you multiply an infinite number by a finite number, it becomes finite? I was thinking this all along, but hesitant to say this.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
x = .999 . . . 2x = 2 x = 2/2, or 1. 2x=2? That assumes .999... is 1. That is wrong anyway. I think it should look like this: x = .999...2x = 1.999... 1x = 1 Again, we are ignoring the last number, because there is no last number. That is what I find to be the problem.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Ok, try it with .5x
x=3.5x=1.5 -.5x= -1.5 That works. x=.999....5x=.4999 (5?)... or maybe just .4999... let's use .4999... -.5x = -.499 x=1.0020040080160320641282565130261 But we are ignoring the 5, can we do that? x=.333....5x=.166... -0.5x=.166 x=? Isn't this proof you can't ignore the last number? Shouldn't the 10x in mod's equation be9.999...0 - .999... be 8.999...1 Edited by riVeRraT, : mistake
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
just as a point and a line are concepts. Concepts exist in time.
Do you accept that between 0 and 100 there are an infinite number of numbers I do not accept it, or not accept it. I think about the possibilities.
Infinite is not a number it means that no matter how far you count, or how many times you divide the line you can still keep counting, still keep dividing, there is no end to it. Now in the universe there may be a limit to how small you can make a division but we are talking mathematics here, pure concept. A concept that has no end. So if the last number of a infinite numver has to change, then we have a problem houston.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
and you still end up with 1 = .999 . . . in that equation. Yes, I know, I was pointing out your mistake. 2*.999... = 1.999...8There is no last number, so we drop the 8 or never put it there. Just like 10*.999... = 9.999...0We drop the zero, or we never put it there, because there is no end. This is opposite of what I am trying to point out. But considered the correct way.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Message 161 Doesn't work according to what your saying.
Don't we have to prove it, or is my math wrong?
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Why did you skip over Message 161 ?
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Are you claiming to be a better mathematician than Newton, Leibniz, Cauchy, Cantor, Godel, Euclid, on and on and on? They were just men like me, maybe with less knowledge of the world, I might add. However, I am not claiming I am correct.
Do you have a problem with Zeno's paradoxs or not? Don't know enough about it yet, I just glanced at it. I mentioned, that is how I always pictured .999... in my head.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
From a quick glance, those equations appear to be slightly wrong. x=3.5x=1.5 -.5x= -1.5 you divide the 1.5 by .5, not multiply by -1, to find out what x is.x = 3, in that equation at the end. Yes, I know, I mentioned that it works.
Here again, you do not multiply by -1. You would divide .499 . . . by .5 to get 1. And you should use .5, instead of .499 . . .. reason being, is that .499 . . . is not half of .999 . . ..(number in line above have recurring decimals) .499 is not even half of .999. .4995 is half of .999 (numbers in line above are finite) I had changed after you replied, go back and look at it. Question, if .4999... can be .5, why can't .333... be .4 ?
You have to divide the .166 . . . by .5 in order to find out what x is. Your missing the whole point then. The first line is subtracted from the second line. You wind up with mistakes, because you never attach a last number.
quote:Repeating decimal - Wikipedia That's because .999 . . . is 1. You are assuming it is 1 before you prove it. Isn't that wrong?If the equation, and the idea of never adding the last number to an infinite set is correct, then it doesn't matter what number we put in front of x in the equation, it should always work, and it doesn't. x should always = 1 if the formula is a valid way of proving .999... = 1
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Using your logic, we could at any point in the equation replace .999... with 1, correct?
x = 0.999...10x = 9.999... (multiplying each side of the above line by 10) 9x = 8.999... (subtracting the 1st line from the 2nd) (using 1) I know what you'll say, and that is 8.999.. = 9
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
Ok, that makes sense.
With unending 9's the difference is zero. But I still don't see why with unending 9's we can't have an unending difference. It's just like admitting infinity doesn't exist.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
If you can show us where the zero is at the end of 0.999... Message 161 Kind of shows how important it is to have that number at the end. In all of kuresu's explanations, he always makes that leap from .999... to 1, or .4999... to .5 If we are going to start changing numbers before proving they are that number, then I have aproblem with it. Even kuresu admits that it is not precise. So I don't see how what I am saying is so off-beat. .4999... * 2 just does not equal .999... Unless you have a 5 at the end of .4999... or you convert it to .5 Just because his calculator says so, doesn't make it fact. It seems to me, there is no valid way of using recurring decimals as part of an equation other being an answer. It's like we are making rules to fit the problem, similar to creationists trying to make the evidence fit their theory. Also, every time we use a finite symbol to represent infinity, an infinite string, we lose what infinite is actually supposed to be.
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riVeRraT Member (Idle past 416 days) Posts: 5788 From: NY USA Joined: |
No, because if we put it into fractions, it makes perfect sense. Its just that decimal representations are a little funny. That's what I said way back in the beginning, that the problem lies within our number system, and decimals being able to express thirds of 10. Of course we can divide 10/3, but how we express it is important.
So, your position is one I can understand. Thanks for your time in explaining all this to me. That's a whole lot better than kindergarden explanations of infinity
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