Gelfond's theorem makes some progress on defining them in light of Hilbert's seventh problem, which asks whether raising an algebraic number not equal to zero or one to an irrational power necessarily produces one of these numbers. The Liouville constant was the first one found because Liouville constructed it to show that a rapidly converging sequence of rational approximations always produces one. The proof of this group's existence explains why squaring the circle is impossible, as it includes  ["pi"] and e. For ten points, name this class including all complex numbers that do not solve any polynomial equation wit
Gelfond's theorem makes some progress on defining them in light of Hilbert's seventh problem, which asks whether raising an algebraic number not equal to zero or one to an irrational power necessarily produces one of these numbers. The Liouville constant was the first one found because Liouville constructed it to show that a rapidly converging sequence of rational approximations always produces one. The proof of this group's existence explains why squaring the circle is impossible, as it includes  ["pi"] and e. For ten points, name this class including all complex numbers that do not solve any polynomial equation with integer coefficients.
Gelfond's theorem makes some progress on defining them in light of Hilbert's seventh problem, which asks whether raising an algebraic number not equal to zero or one to an irrational power necessarily produces one of these numbers.
transcendental numbers