Friedman numbers have density 1

A Friedman number is a positive integer which is the result of an expression combining all of its own digits by use of the four basic operations, exponentiation and digit concatenation. One of the fundamental questions regarding Friedman numbers, first raised by Erich Friedman in August 2000, is how common they are among the integers. In this paper, we prove that Friedman numbers have density 1. We further prove that the density of Friedman numbers remains 1 regardless of the base of representation.