include library query

I have just started to learn programming the Arduino and I am going through some simple examples to get a better understanding. I have just tried an example that uses the sqrt() function, part of the maths group. I couldn't understand why the example had #include "math.h" as the function was listed along with all the rest of the available functions. So as a test I commented out the #include and as I suspected the sketch compiled error free. So whats puzzling me is why it was included and why didn't it error on the #include "math.h" as I don't see that library anyway in the library files. I suspect it may be a throwback from a past version of the IDE, but at the moment it's one of those things bugging me.

math.h is included in the Arduino.h header file, which is included in every .ino file.

math.h is part of the compiler package, not specific to any use of the compiler, such as the Arduino IDE. So, the Arduino package does not (have to) include math.h.

Thank's for the explanations both. I think I am getting my head around ti better now.