What properties do two functions need to hold the distributive property? That is, what's the minimum criteria to be satisfied by functions [math]g[/math] and [math]h[/math] such that:[math]g(x, h(y, z)) = h(g(x, y), g(x, z)) [/math]
Both g and h must be closed binary operations on the same set but that's it. No commutativity, associativity, identity elements, or invertibility are required.
>>16967289Doesn't non-commutation affect left-distributivity?[math]x \div (y + z) \neq (x \div y) + (x \div z)[/math]
>>16967276You cannot reduce the distributive property to something simpler. The minimum criteria needed to satisfy the distributive property IS the distributive property.
>>16967306this
>>16967276they have to be symmetrical.
>>16967306Is there a formal proof for that I can read about somewhere?
