= Algebraic number field
{tag=Quadratically closed field}
{title2=$\overline{\Q}$}
{wiki=https://en.wikipedia.org/w/index.php?title=Algebraic_number&oldid=1168427661\#Field}
The set of all <algebraic numbers> forms a <field>.
This field contains all of the <rational numbers>, but it is a <quadratically closed field>.
Like the <rationals>, this field also has the same <cardinality> as the <natural numbers>, because we can specify and enumerate each of its members by a fixed number of integers from the <polynomial equation> that defines them. So it is a bit like the <rationals>, but we use potentially arbitrary numbers of integers to specify each number (polynomial coefficients + index of which root we are talking about) instead of just always two as for the rationals.
Each <algebraic number> also has a degree associated to it, i.e. the <degree of the polynomial> used to define it.