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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: 05-09-2004


Message 152 of 215 (326089)
06-25-2006 11:36 AM
Reply to: Message 148 by SuperNintendo Chalmers
06-25-2006 10:50 AM


Re: ack
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 answer
2-1+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: 05-09-2004


Message 153 of 215 (326090)
06-25-2006 11:46 AM
Reply to: Message 151 by kuresu
06-25-2006 11:31 AM


Re: Talking about math
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?

This message is a reply to:
 Message 151 by kuresu, posted 06-25-2006 11:31 AM kuresu has replied

Replies to this message:
 Message 155 by kuresu, posted 06-25-2006 11:56 AM riVeRraT has replied
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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 156 of 215 (326095)
06-25-2006 12:01 PM
Reply to: Message 136 by Modulous
06-25-2006 9:55 AM


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:
Some argue that, in the second step of the equation given above, 10x is 9.999...0 and not 9.999... but this is not the case: the right-hand side does not terminate (it is recurring) and so there is no end to which a zero can be appended.
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 = 1.998
You 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.

This message is a reply to:
 Message 136 by Modulous, posted 06-25-2006 9:55 AM Modulous has replied

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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 157 of 215 (326098)
06-25-2006 12:04 PM
Reply to: Message 155 by kuresu
06-25-2006 11:56 AM


Re: Talking about math
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.

This message is a reply to:
 Message 155 by kuresu, posted 06-25-2006 11:56 AM kuresu has replied

Replies to this message:
 Message 158 by kuresu, posted 06-25-2006 12:14 PM riVeRraT has replied
 Message 169 by lfen, posted 06-25-2006 12:53 PM riVeRraT has replied

  
riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 161 of 215 (326103)
06-25-2006 12:30 PM
Reply to: Message 155 by kuresu
06-25-2006 11:56 AM


Re: Talking about math
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 be
9.999...0 - .999... be 8.999...1
Edited by riVeRraT, : mistake

This message is a reply to:
 Message 155 by kuresu, posted 06-25-2006 11:56 AM kuresu has replied

Replies to this message:
 Message 168 by kuresu, posted 06-25-2006 12:52 PM riVeRraT has replied
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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 162 of 215 (326104)
06-25-2006 12:33 PM
Reply to: Message 159 by lfen
06-25-2006 12:28 PM


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.

This message is a reply to:
 Message 159 by lfen, posted 06-25-2006 12:28 PM lfen has replied

Replies to this message:
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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 163 of 215 (326106)
06-25-2006 12:37 PM
Reply to: Message 158 by kuresu
06-25-2006 12:14 PM


Re: Talking about math
and you still end up with 1 = .999 . . . in that equation.
Yes, I know, I was pointing out your mistake.
2*.999... = 1.999...8
There is no last number, so we drop the 8 or never put it there.
Just like 10*.999... = 9.999...0
We 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.

This message is a reply to:
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Replies to this message:
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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 167 of 215 (326111)
06-25-2006 12:49 PM
Reply to: Message 164 by lfen
06-25-2006 12:43 PM


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: 05-09-2004


Message 170 of 215 (326114)
06-25-2006 12:53 PM
Reply to: Message 166 by NosyNed
06-25-2006 12:49 PM


Re: That annoying zero
Why did you skip over Message 161 ?

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 Message 166 by NosyNed, posted 06-25-2006 12:49 PM NosyNed has not replied

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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 171 of 215 (326116)
06-25-2006 12:56 PM
Reply to: Message 169 by lfen
06-25-2006 12:53 PM


Re: Talking about math
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: 05-09-2004


Message 173 of 215 (326120)
06-25-2006 1:05 PM
Reply to: Message 168 by kuresu
06-25-2006 12:52 PM


Re: Talking about math
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:
x = 0.333333...
10x = 3.33333... (multiplying each side of the above line by 10)
9x = 3 (subtracting the 1st line from the 2nd)
x = 3/9 = 1/3 (simplifying)
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

This message is a reply to:
 Message 168 by kuresu, posted 06-25-2006 12:52 PM kuresu has replied

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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 175 of 215 (326122)
06-25-2006 1:08 PM
Reply to: Message 168 by kuresu
06-25-2006 12:52 PM


Re: Talking about math
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

This message is a reply to:
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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 187 of 215 (326146)
06-25-2006 2:30 PM
Reply to: Message 182 by NosyNed
06-25-2006 1:40 PM


Re: .99... = 1 and .33... not = .4 why
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: 05-09-2004


Message 189 of 215 (326148)
06-25-2006 2:42 PM
Reply to: Message 185 by Modulous
06-25-2006 2:14 PM


Re: Zero to heroes
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.

This message is a reply to:
 Message 185 by Modulous, posted 06-25-2006 2:14 PM Modulous has replied

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riVeRraT
Member (Idle past 416 days)
Posts: 5788
From: NY USA
Joined: 05-09-2004


Message 191 of 215 (326150)
06-25-2006 2:46 PM
Reply to: Message 188 by Modulous
06-25-2006 2:31 PM


Re: Infinity in maths is mindbending
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

This message is a reply to:
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