To: UnbelievingScumOnTheOtherSide
"That is illogical. The set of unknowns is infinite. The set of knowns will always be finite. Therefore what is known will never reduce what is unknown." inf = infinity
inf1 = The real number line x from 0 to inf
inf2 = The real number line y from 0 to inf
inf1 = inf2
inf1 + inf2 = 2*inf1 = 2*inf2
inf1 - inf2 = 0
inf1 - some subset < inf1
To: spunkets
inf1 - some subset < inf1Depends on how you define "<" of course. Subtracting a countable subset from an uncountably infinite set (such as you describe) still leaves an uncountably infinte set. Taking all the rationals out of the reals still leaves a set as big as the original reals (in the sense that the sets can be put into 1-1 correspondence.)
Also note that 2*inf1 or 2*inf2=inf2 as does inf2*inf2. It takes power to become bigger.
134 posted on
01/13/2006 6:44:52 PM PST by
Doctor Stochastic
(Vegetabilisch = chaotisch ist der Charakter der Modernen. - Friedrich Schlegel)
To: spunkets
inf = infinity
inf1 = The real number line x from 0 to inf
inf2 = The real number line y from 0 to inf
inf1 = inf2
inf1 + inf2 = 2*inf1 = 2*inf2
inf1 - inf2 = 0
inf1 - some subset < inf1
That is all bunk.
The real numbers is an uncountable set. Removing any denumerable set from an uncountable set does not affect the cardinality of the uncountable set. Therefore since the set of known information is always finite and thereby denumerable and the set of knowns and unknowns is uncountable, subtracting the knowns does not affect the cardinality of the remainder.
But even that is not necessary. If the sum of knowns and unknowns is quantized so that the set is infinite and merely denumerable, subtracting any finite amount from it leaves the remainder in one-to-one correspondence with the original set and therefore of the same cardinality (size).
Now off to remedial set theory with you :-)
Here is a good all-in-one page to explain it to you:
http://www.earlham.edu/~peters/writing/infapp.htm
168 posted on
01/14/2006 2:00:31 AM PST by
UnbelievingScumOnTheOtherSide
(Give Them Liberty Or Give Them Death! - IT'S ISLAM, STUPID! - Islam Delenda Est! - Rumble thee forth)
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