Hello.
If you'd like to read ahead on Linear Algebra I would suggest this book,
http://www.math.brown.edu/~treil/papers/LADW/LADW.html
As for history and development of Mathematics as well as books on geometry I would suggest the books by John Stillwell.
If you are interested in the...
There are a total of 120 combinations with those numbers for you can choose 5 of the entries for the first digit, then 4 for the next, 3 for the next and 2 for the last, thus 5*4*3*2=120.
Fundamental Theorem of Algebra: Every polynomial of degree n (n=/=0) has exactly n roots counting multiplicity over the Complex numbers. In the case of the real numbers, it has d roots where d is less than or equal to n.
For instance, the easiest example x^2+1=0 only has complex solutions...
Well in terms of cardinals, the set of countable infinity has cardinality Aleph-0. The set of reals has cardinality Aleph-1, power set of the reals is Aleph-2 and so on.
Aleph-n is what is called a cardinal number. You could also look into reading about the Generalized Continuum Hypothesis...
So you are asking in which ways you can compare infinities (so the countable infinity and the uncountable infinities).
If this is so, then one way to describe the countable infinity is as the smallest infinity, which is the naturals. Any countable set can be put in a one to one correspondence...