[spunkets]

"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

[Doctor Stochastic]

inf1 - some subset < inf1

Depends 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.

[UnbelievingScumOnTheOtherSide]

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