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Math Help - Is it a finite set ?

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    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.
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