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Comment by melissalobos | Hacker News Reader

One big issue with that notation is that the log of the exponential is not the exponential of the log, so the order really does matter(for any complex valued expressions).

https://www.wolframalpha.com/input?i=log%28exp%28x%2Biy%29%2...

So just having over and underbars loses some information.

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pretty sure that's because log is not well defined over the complex numbers, it's just defined over branch cuts.

similar to how

    sqrt(x^2) != (sqrt((x)^2)

when x is Real but not Positive Real, because sqrt is not well defined over the full Reals.

It's not a flaw of notation, it's a flaw in the attempted math.

I think you mean

  sqrt(x^2) != (sqrt(x))^2

How about we just accept that the square root is a relation inatead of a function?

I am not sure what you mean by "relation" and what the benefit would be. There is a definition for "relation" in mathematics. A function is a type of relation and a relation is a set. But you probably have something else in mind.

Multivalued functions are types of relations. Relations are more general than multivalued functions because relations don't have to be defined on the entire domain.

What’s wrong with the square root, apart from the fact that it’s not defined over all of R? It’s a fairly well behaved function overall.

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