I usually lose any argument with CP, but I'd like to point out that the SQRT(4) can also equal -2, and the SQRT(-4) can equal 2i or -2i.

You are right, but we pick the positive square root just to preserve the property of being a function, that is, each element of the domain is mapped to exactly one element of the codomain. Otherwise, we would violate this principle. My 2 cents.

You probably know this, but I just wanted to clarify.

By the way, I appreciate the macros you contributed to the forums. They have interesting ideas I didn’t have the chance to experiment with. Perhaps in the future.

± is one of many choices in the typing and degree of totality of an implementation (refined definition) of a sqrt function.

If the main function maps to an unsigned set, a secondary function can map each element of the unsigned codomain to a tuple of ± values.

Equally, we can preserve the unique mapping by defining the codomain as a set of such ± tuples.

I was probing in connection with the mathematical terminology rather than trying to understand through metaphor. Your usage of "define" is consistent, and that in itself clears up any uncertainty I had (so I need not go further into where I was coming from on that semantic issue).

And I gather that a *complex point* would be a point on that plane (or not!) that is a *complex number*. Ahhhh...

( Like most *res humanae*, a tuple, or intersection, of real and imaginary components )

All credit to @peternlewis for the work that went into the `%JSONValue%`

token – it's excellent and indispensable.