# Math Help - Show a set is countable

1. ## Show a set is countable

Let E be the set of real numbers, x, satisfying

ax^2+bx+c=0 for some a,b,c in Z

Show that E is countable.

2. Originally Posted by ashamrock415
Let E be the set of real numbers, x, satisfying

ax^2+bx+c=0 for some a,b,c in Z

Show that E is countable.
The cross product of two countable sets is countable. There can be at most two distinct real solutions per (a,b,c). The cardinality of E is at most the cardinality of Z x Z x Z x {0,1}.