We parameterize the set of infinite extended complex numbers (df-bj-ccinfty) using the real numbers (df-r) via the function . Since at that point, we have only defined the set of real numbers but no operations on it, we define a temporary "fractional part" function, which is more convenient to define on the temporary reals (df-nr) since we can use operations on the latter. We also define the temporary real "one-half" in order to define minus infinity (df-bj-minfty) and then we can define the sets of extended real numbers and of extended complex numbers, and the projective real and complex lines, as well as addition and negation on these, and also the order relation on the extended reals (which bypasses the intermediate definition of a temporary order on the real numbers and then a superseding one on the extended real numbers).