A natural number, x, is called a power of ten if there exists another natural number, y, such that 10^y = x. Show that the set of powers of ten is countably inf

Question

A natural number, x, is called a power of ten

if there exists another natural number, y, such that 10^y = x.

Show that the set of powers of ten is countably infinite.

Answer 1

Is it ok to assume that the natural numbers are countably infinite?  If so, you have a one to one relationship given by the equation 10^y = x, where y can be any natural number.

 

Basically since every value of y leads to exactly one value for x, and the y values are countably infinite, so are the x values.