# Thread: Is it a finite set ?

1. ## Is it a finite set ?

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

2. Originally Posted by zhupolongjoe
Which of the following sets are finite and why?

i) {x belong to N: x^2+x is prime}={1}

ii){x belong to N: x is a solution of 4x^8-5x^6+12x^4-18x^3+x^2-x=0}YES

iii){x belong to N: x(10-x)>0}={1,2,3,4,5,6,7,8,9}

iv)the set of all complex numbers a+bi such that a^2+b^2=1
iv) I think this is infinite
iv)the set of all complex numbers a+bi such that a^2+b^2=1
Is the set of all points on the unit circle in the complex plane.