I didn't watch the video for several reasons, so if I was off, I'm sorry. From the comments I couldn't deduce what's actually wrong with the notation, or which notation for that matter. Yes, bad HN ettiquette is to respond anyway.
> If the mention of different domains is about the fact that you can't divide by zero
> I intend all quantities to be drawn from some multiplicative group
That's it. Still, I was trying to draw some hierarchical network, where log and root are both inverses of exp.
In the same way, multiplication is a special case of addition. Although It might not have to be, if it's just my preference to look at it that way. It reminds me of the diamond dependency problem (https://en.wikipedia.org/wiki/Diamond_problem#The_diamond_pr...).
Multiplicative groups to me look like a special case, too. The arrow diagrams look like category theory. I on the other hand just talk from intuition and my experience with the elementary functions, the order I learned in school.
EDIT: Subtraction and division as well aren't associative, so do they really form a subgroup? Another problem besides needlessly complicated notation is ambiguous notation. Wikipedia lists two alternatives for multiplicative groups. One is a special case of a ring which does have a null element. Now, in c/b=a, c can be the null element, but then a would be too, so c/a=b is still undefined. I'd guess that holds for the non-commutative version as well.
> If the mention of different domains is about the fact that you can't divide by zero
> I intend all quantities to be drawn from some multiplicative group
That's it. Still, I was trying to draw some hierarchical network, where log and root are both inverses of exp.
In the same way, multiplication is a special case of addition. Although It might not have to be, if it's just my preference to look at it that way. It reminds me of the diamond dependency problem (https://en.wikipedia.org/wiki/Diamond_problem#The_diamond_pr...).
Multiplicative groups to me look like a special case, too. The arrow diagrams look like category theory. I on the other hand just talk from intuition and my experience with the elementary functions, the order I learned in school.
EDIT: Subtraction and division as well aren't associative, so do they really form a subgroup? Another problem besides needlessly complicated notation is ambiguous notation. Wikipedia lists two alternatives for multiplicative groups. One is a special case of a ring which does have a null element. Now, in c/b=a, c can be the null element, but then a would be too, so c/a=b is still undefined. I'd guess that holds for the non-commutative version as well.