Freaks City

Introduction Consider the following geometric problem: mark all vertical lines x = c and horizontal lines y = c where c ∈ ℤ on a plane. Now consider a line y = (px + r)/q where p, r ∈ ℕ and q ∈ ℕ₊. Since the residue class of r modulo q determines the behavior, we can assume r < q without loss of generality. Imagine a moving point traveling a ...

Consider a labeled monoid (T) acting on an information monoid (S), forming the algebraic structure ((T, \times, 1_T, S, +, 0_S, \circ)). The information monoid ((S, +, 0_S)) satisfies: Closure: (\forall x, y \in S), (x + y \in S). Associativity: (\forall x, y, z \in S), ((x + y) + z = x + (y + z)). Idantity element: (\exists 0_S \in S) such th ...