In the lecture for Week 1, Professor Malan said that in an if statement, the third boolean expression (else if (x ==y)) is redundant or implied, since logically, if it is false that a number is neither greater than nor less than another number, it must be equal to that number.
But I wondered (just logically) is it possible that x could be a complex number, of the form z = x + iy, where the real number x is the real part of z and the real number y is the imaginary part of z and is traditionally plotted "in a rectangular coordinate system called the complex plane" (Briggs, William L.. Calculus: Early Transcendentals. Pearson Education. p. C-1) or displayed in an an Argand diagram which is a plot of complex numbers as points (which is the same thing)?
In that case, then is there another possibility that makes it logically possible for x to not equal y, in the case that it is neither greater than nor less than, but is rather located on the complex plane?
So in this case, am I right in thinking that in order to omit the third boolean expression (else if (x==y)), we have to assume that x and y are real numbers on the real number line, otherwise we may not capture the possibility of it being complex?