Liouville's Number is Transcendental

We prove that Liouville's number, .11000100000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001... = 10^(-1!) + 10^(-2!) + 10^(-3!) + 10^(-4!) + ... is transcendental, so it is not the root of a polynomial equation with integer coefficients. We will need this proof    • Liouville's Approximation Theorem for Alge...   #mikethemathematician, #mikedabkowski, #profdabkowski