Showing that this set of numbers is uncountable is the object of Cantor's (*) diagonal argument.
The possible eigenvalues of a self-adjoint operator lie within this set. No set has a cardinality between that of the integers and this set, according to the continuum hypothesis. Showing that this set of numbers is uncountable is the object of Cantor's (*) diagonal argument. Cubic polynomials have at least one root in this set, but quadratic polynomials are not guaranteed a root in this set. For complex numbers, the "a" term typically is in this set in contrast to the "b" term. For 10 points, name this set of numbers formed from the union of the rational and irrational numbers that is contrasted with the imaginary numbers.
The possible eigenvalues of a self-adjoint operator lie within this set.
real numbers (or reals; do not accept or prompt on “rationals” or “irrationals”)