I have been asked to prove that the cardinality of any algebraic extension of a finite field k is the same as that of Z(the integers)
And if k is not finite, the cardinality of any algebraic extension is the same as that of the field k.
I am not really sure what to do.
If k is a finite field say Fp, then an element z is algebraic over Fp, if it satisfies a polynomial with Fp coefficients say a(0) + a(1)x + a(2)x^2 +....a(n)x^n.
I dont know how to go about it. I was wondering if you could help.