MathDB

Find all non empty subset

S

of \mathbb{N}: \equal{} \{0,1,2,\ldots\} such that

0 \in S

and exist two function

h(\cdot): S \times S \to S

and

k(\cdot): S \to S

which respect the following rules: i) k(x) \equal{} h(0,x) for all

x \in S

ii) k(0) \equal{} 0 iii) h(k(x_1),x_2) \equal{} x_1 for all

x_1,x_2 \in S

. (Pierfrancesco Carlucci)

Problem Statement