the distributive property

[tommy1729]

@MphLee

Hyperoperations, in the general sense, are any sequence of binary operations that includes addition and multiplication. The commutative hyperoperations satisfy this property because \( \exp^0(\ln^0(a) + \ln^0(b)) = a + b \) and \( \exp^1(\ln^1(a) + \ln^1(b)) = e^{\ln(a) + \ln(b)} = e^{\ln(a)}e^{\ln(b)} = a \times b \). That formula is the starting point, it is the definition of commutative hyperoperations. The fact that it contains addition and multiplication can be discussed and proved from the definition.

Andy !

Im honored too see your return at my thread !

However I think your post will not remove MphLee's confusion.

Hope Im more Lucky with my own post.

Maybe you can improve the proof. I dont like it too much now.

regards

tommy1729