User:KBlott/Questions

$(\mathbb N \times \mathbb N, \wedge)$ is a semilattice. $(\mathbb N \times \mathbb N, \vee)$ is a semilattice. Does the first absorption law hold for the protointegers? Does the second absorption law hold for the protointegers? Is $\mathbb N \times \mathbb N$ a lattice? Is the absolute value function a homeomorphism? No. The absolute value function is not a bijection. What are the essential properties of logarithms? What are the commutative monoids on $\mathbb N$? Observe that $e_0≝0, e_1≝ 1^{e_0 }=1, e_2≝ 2^{e_1}=2, e_3≝ 3^{e_2}=9, e_4≝ 4^{e_3}=262144,$ … is the exponential factorial sequence. What essential properties of the protointegers are required to prove the essential properties of the Royal numbers? What are the essential properties of the Royal numbers?