To Infinity, Coachman, and Don't Spare the Horses!

The philosophy of the infinite is infinitely hard to grasp. So the philosophy of infinity is infinitely inadequate, but here goes... What is infinity like exactly? It must be a strange place to visit. If you go to infinity you will arrive at a land where parallel lines meet. Baffling? Infinity is baffling. But some questions about infinity can be solved (chiefly by mathematicians) and pondering the answers is often like having one's skull drilled out and stuffed with writhing trilobites.

Some infinities are bigger than others. In fact we do know what the smallest infinite number is. It is the total of all of the integers, i.e. 0,1,2,3...infinity. This infinite number is called Aleph0. When you add 1 to Aleph0 you do not end up with a larger infinite number. You get the same infinite number. Honestly, this isn't humbug. All this has been proved mathematically to be true. Is the number of positive integers smaller than the combined number of positive and negative integers? No, it is the same size, Aleph0!

There are Aleph0 even integers, Aleph0 odd integers and Aleph0 odd and even integers combined. 2 multiplied by Aleph0 equals Aleph0. Indeed Aleph0 multiplied by Aleph0 equals the same number, Aleph0! There are an infinite number of prime numbers too: there are Aleph0 of them altogether.

But, remember, Aleph0 is the smallest infinite number. Two to the power of Aleph0 is actually larger than Aleph0 and is called Aleph1. This is surmised to be the total number of real (decimal) numbers. (Examples of real numbers are 0.1, -1097.0768, the square-root of two, and pi).



The number of points on a line is equal to the number of real numbers, conjectured to be the infinite number Aleph1. Bizarrely, there is a mathematical proof that shows that this conjecture can never be proved! Incidentally there are as many points on a line as short as the width of an atomic nucleus as on a line spanning the width of the entire universe. This is equivalent to the fact that there are the same number of real numbers between 0 and 1 as between 0 and 1,000,000,000,000,000,000,000,000. Any line contains the same number of points as any other line. This isn't speculation, it is a mathematically proven fact. It was proven by the great Russian Mathematician Georg Cantor. (To digress, mathematically proven facts are true, incorruptible, absolute and unchallengeable).

Cantor was the first to discover that some infinities are larger than others. His ingenious proof is famous in its own right. Cantor also showed that the number of points on a line is equal to the number of points contained in any volume, so for example, the number of points along a pubic hair is equal to the number of points inside the entire Universe.

If some infinities are larger than others then what is the largest infinity of them all? There is another paradox here. Any given set can never be the largest set. This is because the set of all subsets of a set is larger than that set, even if that set contains an infinite number of members. So any given infinite number must be smaller than another. Mathematics forbids the concept of a largest infinite number.

The largest Infinity is like the perfect woman, unobtainable, inconceivable, non-existent, tantalising and... a paradox.

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From:	Hugh Jassovich	Subject:	Cantor	2001-01-24 18:08:35
From:	Rod Gaskins	Subject:	Infinity vs. nothing	2001-12-20 19:40:45
From:	Wu Li	Subject:	Paradoxical Infinity	2003-02-24 08:40:51
From:	liverbean	Subject:	isn't it useless	2003-03-02 14:35:01
From:	jamie	Subject:	zero?	2003-07-18 15:43:06
From:	Clayton Carter	Subject:	A finite headache due to infinity	2003-09-05 18:12:59
From:	ivan	Subject:	its not nothing	2004-02-01 01:31:05
From:	Dakota	Subject:	infinity	2004-03-08 02:11:01
From:	MadPole	Subject:	Main Problem with Infinity	2004-04-24 09:47:26
From:	Clayton Carter	Subject:	My bubble?	2004-08-06 02:34:28
From:	Starhawk	Subject:	The Goddess and infinity	2004-08-21 01:04:56
From:	Benedict Linus	Subject:	a different approach to infinity	2005-03-13 02:12:46
From:	al	Subject:	Islam???!	2005-03-27 15:10:53
From:	Harry J. Burns	Subject:	Kinda funny.	2006-12-06 22:48:39
From:	Harry J. Burns	Subject:	Now is it	2006-12-06 23:14:54
From:	Harry J. Burns	Subject:	My Bad/previous post	2006-12-06 23:20:51
From:	Harry J. Burns	Subject:	sometype of connection	2006-12-07 00:07:09
From:	Rod Gaskins	Subject:	Infinity ain't so big, it's like nothing	2007-02-23 16:31:43
From:	E+L D=aleph0	Subject:	infinite/nothing vs. infinite/everything	2008-03-19 19:12:58
From:	E+L,D=aleph0	Subject:	Existance+life=death=aleph0, given time	2008-03-19 19:38:41
From:	E+L,D=Aleph0	Subject:	to clarify....	2008-03-25 05:18:03
From:	ed zunz	Subject:	infinity and religion	2008-12-16 21:24:02
From:	Rod Gaskins	Subject:	Nothing to Infinity	2009-03-24 06:14:58
From:	Rod Gaskins	Subject:	Breakthrough in infinity!	2009-09-30 05:56:44
From:	Rod Gaskins	Subject:	Breakthrough in infinity!	2009-09-30 05:57:50

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