Question

can i count in complex numbers?
why not?

Answer 1

Hm good question, my first thought was that it has something to do with the Dimensions of complex numbers.

Answer 2

But that thought is when it comes to functions, I am not sure if it can be applied in here.

Answer 3

so complex numbers have 2 dimensions right? a real dimension \(\mathcal R\), and an imaginary dimension \(\mathcal I\),

Answer 4

yes @UnkleRhaukus

That's how I would have started.

Answer 5

So we know how a complex number can be portrayed using polar coordinates, we can add (count) them with simple vector geometry, but all these steps are two dimensional.

Answer 6

i suppose irrational numbers are uncountable, so too are complex numbers ?

Answer 7

Yes, cantor showed that irrational numbers are uncountable, I agree.

Answer 8

there is an infinite set of both complex and real numbers.

Answer 9

http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

Answer 10

No.
Examples of countable sets include the integers, algebraic numbers, and rational numbers. Georg Cantor showed that the number of real numbers is rigorously larger than a countably infinite set, and the postulate that this number, the so-called "continuum," is equal to aleph-1 is called the continuum hypothesis. Examples of nondenumerable sets include the real, complex, irrational, and transcendental numbers.
http://mathworld.wolfram.com/CountablyInfinite.html