text: All fields with characteristic zero contain a copy of this field.
full_question: All fields with characteristic zero contain a copy of this field. The cardinality of this set can be established by writing each element in a big square, then moving diagonally down the square to count them. The larger completion of this set can be constructed from it by partitioning it, then taking the least upper bound of the lesser partition. (*) Algebraic numbers are the roots of polynomials whose coefficients come from this set. This set is the starting point for doing Dedekind cuts, and it is dense in the reals. The set of all of these numbers is denoted Q, and they have eventually repeating or terminating decimal expansions. For 10 points, identify these numbers, which, for integers a and b, can be written as the fraction a over b.
first_sentence: All fields with characteristic zero contain a copy of this field.
raw_answer: Rational Numbers