Which of the following sets are finite and why?
i) {x belong to N: x^2+x is prime}
ii){x belong to N: x is a solution of 4x^8-5x^6+12x^4-18x^3+x^2-x=0}
iii){x belong to N: x(10-x)>0}
iv)the set of all complex numbers a+bi such that a^2+b^2=1
I know a set is finite if it is empty or if it is equivalent to Nk, but I am having trouble applying this.
Here is my attempt:
i) finite since it can be equivalent to Nk
ii) I suppose it is finite due to the number of solutions
iii)finite...same?
iv) I think this is infinite