These numbers that contain the irrational numbers can be written using infinite decimals.
The Vitali Set is a non-measurable subset of this class. Axiomatized by Alfred Tarski, this class can be considered as equivalence classes of Cauchy sequences which can be used to see that each Cauchy sequence converges. It has the least upper bound property in that any set bounded above has a supremum, and this complete metric space can be constructed using Dedekind cuts. As shown in Cantor's diagonalization argument it has an uncountably infinite number of elements. These numbers that contain the irrational numbers can be written using infinite decimals. For 10 points, name these numbers that are not imaginary, represented by a capital R.
The Vitali Set is a non-measurable subset of this class. Axiomatized by Alfred Tarski, this class can be considered as equivalence classes of Cauchy sequences which can be used to see that each Cauchy sequence converges.
real numbers (accept R before mentioned)