User blog comment:Sbiis Saibian/Googology101 - Part II/@comment-10429372-20141024190431/@comment-5982810-20141025183113

@LP9

" You mention function |10^(x+iy)|=|x+iy|, but in what parameter is this function? x? y? Both? "

Typically we define functions by establishing an independent variable (usu.x) and a dependent variable (usu.y). However what I have provided here is called an implicit function. The solution set, the set of values (x,y) that satisfy the equation is what I'm talking about. In this case neither variable is really independent of the other. You can choose one and then solve for the other. It is worth noting that when we define such things implicitly like this, there is a chance that what we have is not technically a function, because for a function every value of x must imply a single value of y. In this case there are actually 2 solutions for y, a negative and positive value. In this case we use the more general concept of a "relation" which is any set of points in the plane, of which "functions" are just special cases.