MathDB

Three operations

f,g

and

h

are defined on subsets of the natural numbers

\mathbb{N}

as follows:

f(n)=10n

, if

n

is a positive integer;

g(n)=10n+4

, if

n

is a positive integer;

h(n)=\frac{n}{2}

, if

n

is an even positive integer. Prove that, starting from

4

, every natural number can be constructed by performing a finite number of operations

f

g

and

h

in some order.

[

For example:

35=h(f(h(g(h(h(4)))))).]

Problem Statement