Sorin Petcu (8/8/2008)
The Square Root of -1 is i, which is an imaginary/complex number."The computer didn't know nothing about complex numbers. You assume that SQRT function, which is written by a computer programmer, should return i for -1 argument. Why? you wrong here. I could write my SQRT function how my muscles want. It is about programming and not about theory. Negative numbers are represented in computer different way by the way you know from theory. So, please don't mix the math theory with what is inside a computer.
We're not talking about negative numbers, negative numbers are just the input to a function, we're talking about the output of the function.
The Square Root of a Negative number (the output of the function) is represented in mathematics as an imaginary (pure) or complex (mixed a +bi) number.
The SQRT function used by SQL server returns a float. The Float data type is not able to contain a complex number. Thus the return data type of the SQRT of -1 is out of the domain of the float data type and we get an error message. How the function determines this (either it actually tries to calculate it and gets an error after attempting to find this value, or if it throws the error as soon as it sees the negative I don't know.. and frankly, I don't care).
I do know that -1 * -1 = 1 and that SQRT(1) = +/- 1.
If you think that SQRT(-1) is a negative number... tell me what negative number squared yeilds a negative number, because what I was taught in math was that -1*-1 = 1. In fact,
SELECT -1 * -1
On my SQL box that returns 1, not -1. So -1 Squared = 1... and SQRT(-1) is a domain error.
If you write your SQRT function to behave in a way that violates how mathematics work, then your company wouldn't be able to sell the software.
That would be like if I decided that my multiplication function should randomly divide all results by .75 because I feel like it. Yah I could write that function, but nobody would sell it, and if they did, it would be acknowledged as a bug (see Intel chips with broken floating point mathematics circa 1994), in the case of software like SQL server this would result in a hotfix released because if your math functions don't follow the rules of mathematics, then companies don't use them.