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Author Topic:   A question of numbers (one for the maths fans)
lfen
Member (Idle past 4678 days)
Posts: 2189
From: Oregon
Joined: 06-24-2004


Message 196 of 215 (326163)
06-25-2006 4:06 PM
Reply to: Message 192 by riVeRraT
06-25-2006 2:53 PM


Re: elementary algebra
Infinity cannot be used in regular equations.
Bingo! Infinity is not a quantity. As for the convention of [...] it
is well defined and presents no problems when used by mathematicians. I think the problem is you are trying to use very simple algebra and are getting some of the conventions wrong. I like your idea of taking some math classes. Just Do It!
lfen

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


Message 197 of 215 (326227)
06-25-2006 11:23 PM
Reply to: Message 99 by RickJB
06-24-2006 5:43 AM


Well I used to smoke, but for 2.5 years now. It was a casual thing anyway, but not when I was younger.
Tell me, what stoner doesn't wonder about infinity?
Anyway, let me just clear up what I meant, I think cavediver knows what I was hinting at.
I could tell you about God all day, and it will never be anything more than subjective, and subjectively He could exist. You won't know He exists until you experience something objective.
Same thing with infinity. We can talk about it all day, and say things like, well imagine the biggest number you can, now add 1, it never ends. But if we apply that to objective things, and start counting, then it becomes another story. we just don't know if infinity will ever exist but inside our own subjective minds.
Look, there is a possibility, that it may not even exist subjectively, just look at .999... it is actually 1. But this is a different kind of infinity. But to me, it just shows what can happen when you have too many numbers.

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Replies to this message:
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 Message 200 by lfen, posted 06-26-2006 3:18 AM riVeRraT has replied

  
SuperNintendo Chalmers
Member (Idle past 5834 days)
Posts: 772
From: Bartlett, IL, USA
Joined: 12-27-2005


Message 198 of 215 (326235)
06-25-2006 11:39 PM
Reply to: Message 197 by riVeRraT
06-25-2006 11:23 PM


good point
we just don't know if infinity will ever exist but inside our own subjective minds.
You may be correct in a general sense. Of course the infinity we are discussing here is a mathematical concept created by humans so it certainly exists as an abstract concept
It's like a word... Does a word really exist outside of the abstract concept of language?

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


Message 199 of 215 (326246)
06-26-2006 12:10 AM


We are not alone
Talk - Wikipediaroof_that_0.999..._equals_1
I just realized that wikipedia has discussions. Don't worry, I'll leave it alone.
Edited by AdminModulous, : disabling smilies because Talkroof was sticking its tongue out

  
lfen
Member (Idle past 4678 days)
Posts: 2189
From: Oregon
Joined: 06-24-2004


Message 200 of 215 (326307)
06-26-2006 3:18 AM
Reply to: Message 197 by riVeRraT
06-25-2006 11:23 PM


Too Many Numbers!!!
But to me, it just shows what can happen when you have too many numbers.
That is a hilarious statement. Should we pass a law limiting numbers to no more than a googal, a million?
This is sort of a variation of trying to pass a law making pi=3.14! or something.
lfen

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


Message 201 of 215 (326320)
06-26-2006 5:44 AM
Reply to: Message 200 by lfen
06-26-2006 3:18 AM


Mind full
That is a hilarious statement. Should we pass a law limiting numbers to no more than a googal, a million?
This is sort of a variation of trying to pass a law making pi=3.14! or something.
It's funny, I know, I laughed when I wrote it.
But think about it. does .999... even exist? I asled that earlier in the thread. Maybe it cannot exist, because it is 1.
Look at converging series, another funny thing that happens when you too many numbers.
From an ignorant view, it looks like anytime we have all these numbers in a row, our minds can't handle it, so we make hillarious rules to make the numbers fit into our minds.

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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 202 of 215 (326326)
06-26-2006 6:11 AM


recurring quotation!!
Edited by AdminAsgara, : took out ridiculously long set of quote tags to fix page width

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sidelined
Member (Idle past 5908 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 203 of 215 (326423)
06-26-2006 11:21 AM
Reply to: Message 202 by riVeRraT
06-26-2006 6:11 AM


Re: recurring quotation!!
riVeRrat
Recurring but finite.

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 204 of 215 (326551)
06-26-2006 5:26 PM
Reply to: Message 203 by sidelined
06-26-2006 11:21 AM


Re: recurring quotation!!
Is 1 finite?

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 205 of 215 (326572)
06-26-2006 5:53 PM
Reply to: Message 204 by riVeRraT
06-26-2006 5:26 PM


Is 1 finite?
Yes

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PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 206 of 215 (326579)
06-26-2006 6:04 PM
Reply to: Message 201 by riVeRraT
06-26-2006 5:44 AM


Re: Mind full
quote:
From an ignorant view, it looks like anytime we have all these numbers in a row, our minds can't handle it, so we make hillarious rules to make the numbers fit into our minds.
From a more educated point of view, the rules for summing infinite series make perfect sense. Our understanding if the integral calculus is based on them (and that's a very useful bit of mathematics).™

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


Message 207 of 215 (326679)
06-26-2006 10:51 PM
Reply to: Message 206 by PaulK
06-26-2006 6:04 PM


Re: Mind full
Yea, yea, I know, I can't wait to actually learn it.

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Replies to this message:
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lfen
Member (Idle past 4678 days)
Posts: 2189
From: Oregon
Joined: 06-24-2004


Message 208 of 215 (326708)
06-27-2006 1:24 AM
Reply to: Message 207 by riVeRraT
06-26-2006 10:51 PM


Re: Mind full
Well, Rat, you never said, did you get the intuitive explanation based on Zeno? That since we can cross a distance of one even though we go through infinite number of points then the sum must exist?
lfen

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Replies to this message:
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PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 209 of 215 (326714)
06-27-2006 2:31 AM
Reply to: Message 207 by riVeRraT
06-26-2006 10:51 PM


Re: Mind full
The math I am talking about (Real Analysis and the Theory of Limits) is basic undergraduate stuff. My first exposure to the Integral Calculus was before University. If your math skills are up to it then you should be able to find textbooks covering it.

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


Message 210 of 215 (326991)
06-27-2006 10:32 PM
Reply to: Message 208 by lfen
06-27-2006 1:24 AM


Re: Mind full
I have been pondering this whole thing, ever since the thread started.
Most of what I came up with aside from a few errors, is not new, and still argued about today. For practical purposes, and to make calculus a reality, I guess the formulas are good enough. I don't know enough to even say that.
My main question, is, does infinity exist. Like Nosy pointed out, we have been talking about 2 kinds of infinity. One that goes on and on, and the recurring decimal kind.
To me, if .999... can equal 1, then there is a limit to how many recurring 9's you can have. What bothers me, is that this only happens with 9 in a 10 base number system. If we were using a 3 base number system, then .222... would equal 1. .999... in a 12 base system would not equal 1, it would just be .9999... I was wondering if there was a way to make a forumla using to different bases to prove something.
I think I understand Zenos problem, in that the gap between .999 and 1 becomes infinitly smaller as you go. Something that is infinitly small doesn't exist, right? If that's true, I tend to disagree. To say it doesn't exist puts it at an end.
On that same note, I was thinking about an explosion in infinite vacum. The particles head out, and are on a infinite path, and will just keep going and going. But one problem is that they will always be a finite distance from their starting point, and from each other, no matter how far they go, to infinity.
I start seeing a lot of relavance between time and infinity. They say we are talking purely numbers. But every number we blurt out of our mouths, comes at a certain time. There is even a discussion about it in wikipedia, and it matches what I was saying.
.999... / 2 = .499...5
They say, how can you add a finite number to the end of an infinite string? I don't know, but I feel it needs to be there, I just don't know how to prove it, and it could take me years, and I may never be able to prove it.
I can say this. .999... = 3/3
Of course 3/3=1.
.333... never resolves to anything, but it does, it resolves to 1/3.
Just like .999... resolves to 3/3.
It's all fine and dandy, if we are talking about thirds of one. Of course three thirds = one.
That's why I was asking the question, does any two numbers multiplied together equal .999... I wanted to see if I could use that in an equation to prove that .999... can also not=one.
But, as I write this, I just thought of something.
.44 +.55 = .99
But .444... + .555.. =1
Can .444... or .555... be sum of any multiplier?
Do these numbers even exist, but on paper? As a concept?
What's the point of converging numbers anyway, from a purely number point of view. Why can't a series of numbers just continue forever? Why can't it just get infinitly smaller, who cares, they are just numbers.
Of course I see the practicality of it in the real world, but not in an imaginary number world.
Ok, my head hurts, going to sleep, I am probably too tired to even be writing this stuff.
Infinity is actually the way in and out of our universe.

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Replies to this message:
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 Message 212 by lfen, posted 06-28-2006 2:25 AM riVeRraT has replied
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