🚀 go-pugleaf

The Silent Observer <silent1@ix.netcom.com> writes:

>The rule, in my mind, has always been "you have to square infinity to 
>make it any bigger."

	That's not quite it...if you think about it, the rationals could
be looked on as a 'squaring' of the integers, for instance. If you think
of the integers as the points on a number line, then you can think of the
rationals as points on a grid: the point (p, q) corresponds to p/q. 
Geometrically, it's reasonable to think of the rationals, written this way,
as a squaring of the integers. Squaring an infinity leaves you with the 
same old infinity all over again.

	To make a bigger infinity, you have to look at something called the
"power set." If you have a set--we'll call it A, even though its name is
actually something like Q or G--then you make the power set of A by making 
a new set--which we'll call Lucky David as that is not its name--that 
consists of all the subsets you can make out of A, which, while we were
not looking at it, went and changed its name to Mildred.

	So, for instance, if the set A (Q)(G)(Mildred) was just the set:
	{ 1, 2, Cincinatti, 4}

	Then the power set of A (Q)(G)(Mildred), which we know of as Lucky
David, would be the set:
	{ {1}, {2}, {Cincinatti}, {4}, {1, 2}, {1, Cincinatti}, {1, 4},
	 {2, Cincinatti}, {2, 4}, {Cincinatti, 4}, {1, 2, Cincinatti}, 
	 {1, 2, 4}, {1, Cincinatti, 4}, {2, Cincinatti, 4}, 
	 {1, 2, Cincinatti, 4} }

	This is a much bigger set; if you want to prove this, you can use
something that looks just like Cantor's argument about the uncountability
of the reals, but which in fact is just like Cantor's argument about the
uncountability of the reals.

	But by taking a power set on an infinite set, you get a new
infinite set, whose name is being withheld to protect our sources, that 
is much bigger.

								Joseph Nebus
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	It's probably not a good idea to go from a Robert Benchley web site
right into alt.folklore.urban without decompressing first.