View Single Post
Old 11-06-2012, 10:51 AM   #17
Claudius
Professional
 
Claudius's Avatar
 
Join Date: Jun 2009
Posts: 1,023
Default

It has do with the fact that the complex numbers isn't an ordered field. The real numbers is either constructed from the rational numbers as dedekind cuts (look this up), or as equivalence classes of Cauchy sequences of rational numbers. You make R into an ordered field by saying a < b for two dedekind cuts a and b, if a is contained in b. (dedekind cuts are sets).

If follows by the axioms of an ordered field, that for any nonzero element x in the field
x^2 > 0. Now , since i^2 = -1, you see why it can't be a real number.

Last edited by Claudius : 11-06-2012 at 11:00 AM.
Claudius is offline   Reply With Quote