Stupid Hypocritical Number

So the other day I was reading one of my political blogs. I forget the topic of the day (or hour maybe), but at the top there was an advertisement that caught my eye. There was an advertisement for a shirt that basically looked like this:



I shouldn't explain this, but I have to because it angers me. Sure at first glance it's cute, or intelligent or whatever. You see a rational number is a fraction of integers (integers are whole numbers like 1,2,3,...), and Pi is not a rational number (an irrational number). So i is telling Pi to be rational. On the other hand i is an imaginary number (if you don't know what that means then just nod your head, or screen). Thus Pi is telling i to be real. This is all fine and dandy except that Pi being a real number has a place to tell i to be real. BUT i isn't rational!?! At best i is an algebraic integer (I'm sure everyone wants to know that) or just algebraic. The point is that while i could tell Pi to be algebraic, it i has no place telling Pi to be rational! Hence it is a stupid hypocritical number!

Note: I realize that there are ways that i can be considered "rational". For example the set Q[i] is called the Gaussian rationals, hence any element of Q[i] is a Gaussian rational. Thus i is a Gaussian rational. The problem with this is that if you want to use an extended definition of rational we can just as easily say that Pi is R-rational and hence rational. In this case i is no longer hypocritical, but just bigoted.