We have card (Real Numbers) = c, and this is also the cardinality of the Real

numbers in the interval (0,1). The numbers in this interval is constructed from

arbitrarily long strings of numbers in arbitrary combinations. So:

c = card (0,1) + card (0,1) + ....

with a term for every natural number, therefore:

c = c*(aleph_0)

while for k a constant: k^(aleph_0) is constructed from arbritarily long strings

in only one combination, therefore:

c*(aleph_0) = c > card (k^(aleph_0))

Then card (k^(aleph_0)) is either < or = aleph_0 since Cantor proved there is no

other cardinal between the two. Is there another cardinal < aleph_0 except

card (0)?

Is the cardinality of an infinite sum equal to the cardinality of it's largest term if

this term is infinite and the rest are smaller?

Is the cardinality of a complex variable (s) tending (somehow) to infinity equal to

the cardinality of |s| for Re (s) tending to infinity?

For the statement:

lim (s -> s_0) F(s) > G (s_0)

if we only have that F(s) has a simple pole at s_0 while G (s_0) may or may not

have a pole there and card (LS) = c while card (RS) = card k^(aleph_0) can we

conclude that the statement is true for all F(s) and G (s) with this property no

matter where the pole s_0 is located?