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Zero and Infinity
    #382072 -

There is an infinite amount of zeroes.

1 -1 + 1 - 1 + 1 -1 + 1... (ad infintium)
= 0 or 1
----------> = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1)... = 1
or --------------> = (1 - 1) + (1 - 1) + (1 - 1)... = 0
WTF?!?! This infinite series can equal 1 or 0. And since each series is identical, logic just breaks down, because zero plus zero can suddenly equal one, and one plus zero can suddenly equal zero.

you can use any arbitrary series

5 - 5 + 5 - 5 + 5 - 5...
= 5 + (-5 + 5) + (-5 + 5)... = 5
or = (5 - 5) + (5 - 5) + (5 - 5) = 0

If the smallest particles are atoms (or subatomic particles, or subsub...) and they can move freely, then there must be a void; a nothingness. How much nothingness is there? Infinite would seem to be the answer, for:
0 * (any number) = 0, but 0 * infinity = 1 (?)
[in projective geometry, 1/0 = infinity and 1/infinity = 0, so 1 = 0 * infinity; or look at it as a/b = c and a/c = b, in both cases, a = bc)

1 is the only number that is safe from being sucked into zero or cast off into infinity when raised to a power. Square it, cube it, root it. It stays there, at one, all the other numbers increase or decrease.

Edited by Kid on 08/30/01 11:37 AM.


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Re: Zero and Infinity [Re: Kid]
    #382090 -

compromise is a good word...
becoming one



Love.
Destroy the ego free the real self.


--------------------
Evolution of Time.

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Re: Zero and Infinity [Re: Droz]
    #382633 -

Here's another bizzarro one.

Let a and b both be equal to 1.
(^ - to the power of)
(_/`` - root)

b^2 = ab
a^2 = a^2

subtract the two equations from each other
b^2 - a^2 = ab - a^2 [next step, add a^2]
b^2 = ab [yes, I know this is above, but watch, subtract ab now]
b^2 - ab = 0

now use the quadratic formula

b = -a +/- _/``a^2 + 4(1)(0) [since the "c" here is zero]
--------------------------------
2

b = 1/2 * -a +/- _/``a^2
= 1/2 * -a +/- a [-a + a = 0 and -a - a = -2a, one half of which is -a]
= 0 or -1

therefor, b is equal to zero or negative one, despite the fact that it begins as a one. No dirty tricks are being played in this equation as far as I can tell, but plugging in the value only works for zero, so it seems that zero works as well as one.

another way of doing it

b^2 - a^2 = ab - a^2 [factor]
(b + a)(b - a) = a(b - a) [divide by b-a]
b + a = a [subtract a]
b = 0
so again one becomes zero. The only dirty trick being played here is dividing by b-a, because b-a=0, and of course, dividing by zero is nonsense.

Edited by Kid on 08/31/01 09:35 AM.


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Re: Zero and Infinity [Re: Kid]
    #382663 -

Shit, I studied A-Level pure maths... I used to be able to understand this stuff... Hang on, I'll get there in a minute...

I'm not sure that it's valid to use an equation with the same formula on each side in a proof, as it cancels it's self out, which is why you return to b^2=ab after combining the two equations.

Hmm... Need my books...


take care



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Re: Zero and Infinity [Re: Kid]
    #382667 -

"This sort of thing has come up before... and it has always been due to human error." - HAL 9000

"I hate to say this, but this place is getting to me. I think I'm getting the Fear."


--------------------
Don't squeeze the pancake batter

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Re: Zero and Infinity [Re: Kid]
    #382981 -

if
b^2=ab
then
a=b


Heres a shitty number for you to contemplate: -0
Yes -0 does exist it is a number, its when you continuously get closer to zero from the negative side but you never actually reach zero, so its still zero but its negative.

Heres another evil of the devils language (aka Math) 1/3=.33333333333333333.......
2/3 =.6666666666666666.......
3/3=1
therefore 1/3+2/3=.99999999999999999............. which is equal to 3/3 which is = to 1. Crazy but true.

Novelty


--------------------
Vote Jonnyshaggs in the next election for GOD...Its the responsible choice

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Re: Zero and Infinity [Re: jonnyshaggs420]
    #382993 -

Heh, yeah, Kid, my algebra II teacher had that "proof" that 1=0 in her room, and you're right, it's invalid because you are dividing by zero.

I'm not entirely sure that infinite series thing works...things get really hairy when you use infinity, because there is no end. So, if you had an infinite series of 1 and -1 pairs, it wouldn't matter if you used the associative property to leave out the first 1, there would be a -1 that would pair off with it, otherwise it wouldn't be an infinite series. As for the 2/3 + 1/3 = 3/3 thing, that's exactly why you leave numbers like 2/3 in fraction form. The decimal form of 1/3 or 2/3 is not exact, it's just an approximation. Again, infinity is weird shit.

Another weird thing to think about is that 1 and infinity are the only two numbers that when raised to any power equal themselves...of course infinity isn't a true value, but oh well.



Remember I'll always love you as I claw your fucking throat away. It will end no other way.
-Tool


--------------------
Remember I'll always love you as I claw your fucking throat away. It will end no other way.
-Tool

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Re: Zero and Infinity [Re: feign]
    #383173 -

out of left field I think it is a question of conformity and diversity or, novelty and retention. The vacume attracts things to it, images and ideas, concepts, information. I don't know much math, but I had an intuition once that geometry is the "natural" mathmatics, whatever the fuck that means.



--------------------
my vocabulary did this to me

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Re: Zero and Infinity [Re: feign]
    #383194 -

That's what's bizzare about these numbers. Logic just breaks down completely when fucking around with them, but we find infinities and zeros (or near zeros) in physics, calculus, and projective geometry. They have useful applications but don't make much sense.


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Re: Zero and Infinity [Re: feign]
    #383255 -

Actually the fraction form is more of an approximation, and it makes the number easier for us to understand as well.

Novelty

http://www.shroomery.org/bluethumb/


--------------------
Vote Jonnyshaggs in the next election for GOD...Its the responsible choice

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Re: Zero and Infinity [Re: jonnyshaggs420]
    #383265 -

mmmmmmm, not really. a/b where b does not = 0, is used to denote the set of rational numbers. Now, irrational numbers are represented in such ways as pi or as the square root of 5. A rational number is accurate, in that it represents its own value.


Now, here's an interesting equation discovered by Euler: (the letters on a keyboard can't represent it)

e (energy) to the power of [i (square root of -1) * (times) pi (3.14...)] = 0.

Someone try showing me the proof for that

e^(_/``-1 * 3.14...) = 0


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Re: Zero and Infinity [Re: feign]
    #383275 -

The infinite series thing I'm not too sure about either. I think it was Zeno who came up with the paradox about Achillies racing the Tortoise, and showed that Achillies could never catch up to the Tortoise by adding up one half of the previous time/distance travelled. The problem is solvable by prooving that the distance that Achillies travels, even though when summed through the infinite series has no end, approaches 2 (that is, adding up the halfs will never hit 2, but it approaches 2 infinitely). With the above infinite series, I'm not certain what the series approaches.


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Re: Zero and Infinity [Re: Kid]
    #383369 -

its all in limes.....but you can not find limes for something fluctuating such as +1-1+1-1 because it has two "peeks" so anyway---you are putting infinity in places where is no logic to put them there.

afterall you are all good people sometimes
~Crobih

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Re: Zero and Infinity [Re: Kid]
    #383377 -

mistaking the tools for the house. the potentiality for the reality. can we say math is primarily measurement? that is, I guess, a ruler still measures a foot even if that measurement isn't applied to an object. measuring space (matter) and time (as a representation of eternity, infinitely small or large, positive or negative) . Our amazment (a-maze-ment, i.e. confusion) is with finding order. If we find order, what does that mean. You go on a chase like that movie pi? Get a taste of the glory of discovery, and the famished brain, devoid of meaning and substance goes on a feeding binge. Aren't computers programed entirely with 1's and 0's. In this case a computer is a better solution than an abstracted philosophic meaning. A computer is where the meaning of the number chase is stored, objectified, literally.



--------------------
my vocabulary did this to me

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Re: Zero and Infinity [Re: inbetween]
    #383482 -

still, it does seem intuitively obvious that
0/1 x 1/0 = 1
(zero times undefined(infinite) equals one...
i know it is an illegal operation, but it should work out, 'cause... well, here we are...

old enough to know better
not old enough to care


--------------------
old enough to know better
not old enough to care

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Re: Zero and Infinity [Re: jonnyshaggs420]
    #383490 -

1/3 = .333... 2/3 = .666 and 3/3 = .999... there is no number between .999... and 1 so they must be the same number. thats not very funky

Tangerine trees and marmalade skies...


--------------------
Tangerine trees and marmalade skies...

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Re: Zero and Infinity [Re: gnrm23]
    #383493 -

that does seem like 1 being the loneliest number or some such nonesense from the 60's. Which does feel fairly sublime right about now. thanks for the reality check. needed it. good will to you gnrm23. I'm a goddamned manic-depressive and sometimes skip over the obvious, especially in public contexts.



--------------------
my vocabulary did this to me

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Re: Zero and Infinity [Re: inbetween]
    #383519 -

Somebody posted in this thread that geometry was the only true math (or something along those lines), but even geometry can break down into silliness. Say you own a farm, shaped like a right angle triangle, and the two sides are 50 meters each. How long is the other side? _/``5000. What's the sqaure root of 5000? Well, it's an irrational number. No matter how small you make the marks on your ruler, you can't ever get there. Now that's absurd!


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Re: Zero and Infinity [Re: Tamrylin]
    #383523 -

What else is cool about infinity is:

The set of all rational numbers (numbers which can be expressed as a/b where b does not = 0) is infinite. (a and b can be any number, moving up and up or down and down, ad infintium). So, the set of rational numbers is infinite, but we all know that the set of rational numbers is not all numbers. So, it seems that the infinite carpet covers both the set of rational numbers, plus all other numbers.
It's almost like their is a hierarchy of infinities (some mathematicians have come up with ways to represent this problem, such as a countable infinity sign and an uncountable infinity sign).


Nonsense, nonsense I tells ya!


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Re: Zero and Infinity [Re: Tamrylin]
    #383524 -

That's another one of those questions that would've bothered the Greeks.

I own one meter of farm, but due to some dispute, you are entitled to one third of it. You will, never, never, get exactly your one third. It just can't be represented on a measuring stick.


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