How can we show that Z (a set of integers) is a proper subset of A?
A = {x is an element of R | {x,x^2,x^3,......} intersection of Zis not equal to the empty space}. I just need a way to start the problem I can do the rest. The only thing that's throwing me off is the intersection of Z. Thanks.
2007-01-14 05:09:23 · 3 answers · asked by Johnny O 1 in Science & Mathematics ➔ Mathematics
One way to see this is given A is set of roots to finite degree integral coefficient polynomials, note that Q is the set of roots to degree one integral coefficient polynomials and Z is the set of roots to to degree one integral coefficient polynomials, for which the coefficient of x is 1. Thus Z is a proper subset of Q which is a proper subset of A.
2007-01-16 04:22:01 · answer #1 · answered by Phineas Bogg 6 · 0⤊ 0⤋
A = set of powers^(integers)
Z = set of integers
empty space means that there is no element contained in one that is present in the other (which is not the case here).
if x is an integer the A will be subset of Z. If x is a rational number (4.1023) then no.
2007-01-14 05:26:37 · answer #2 · answered by Dr Dave P 7 · 1⤊ 0⤋
This makes little sense. Could you be more clear?
2007-01-14 05:17:29 · answer #3 · answered by gianlino 7 · 0⤊ 0⤋