Show there is a symmetric monoidal structure on \((\mathbb{N}, \leq)\) where the monoidal product is \(6*4=24\). What should the monoidal unit be?
Let the monoidal product be the standard product for integers, with 1 as unit.
Monotonicity: \((x_1,x_2)\leq (y_1,y_2) \implies x_1x_2 \leq y_1y_2\)
Unitality: \(1*x_1=x_1=x_1*1\)
Associativity: \(a*(b*c)=(a*b)*c\)
Symmetry: \(a*b=b*a\)