mtassin (8/8/2008)
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 think you don't understand or you don't want to understand.
Let me see: how it is represented the number -5 in computer? as binar form as 1111111111111111111111111111111111111111111111111111111111111011 and this number would be reconverted as 18446744073709551611 in decimal format.
So, SQRT(-5) would be what? guess what:
select SQRT(18446744073709551611) = 4294967296
So we are talking only about numbers and not math theory. You said forth and forth about complex numbers. Wrong! Why you want to receive a complex number from a function built in a programming language? Why you want all the time that float number can't be asimilated as complex number? It is nothing to do with complex numbers in a programming language or an engine like sql server. Complex numbers are in math theory. So wake up!