Weird question

>F^2 = not fag
>Lets say he can go on as long as he wants.
>So the question is, what state is F^F equals to ?

You're implying there is some strict order on a set of values that, in any case, includes all natural numbers as well as F, and that F comes at some point in this order (1 < 2 < ... < F).

Unless you further specify this structure, we'll not be able to makes sense of F^F.

The first approach or framework that comes to mind:
If you take a category of sets, you can discard all isomorphisms (for sets, those are bijections) and obtain a class of cardinals. In this category, basic limits induce cardinal alrithmetic.
So for example, take the sets A={7,8} and B={3,4,5}. Then |A| = 2 and |B|=3. The product AxB is isomorphic to the set
P = {<7,3>, <7,4>, <7,5>, <8,2>, <8,4>, <8,5>}
with |P| = 6
That is to say
|AxB| = |A| x |B|.
The exponentiation is induced by considering function spaces.
E.g. B->A, internally writte A^B, has elements such as
f = {<3,7>, <4,8>, <5,7>}
or
g = {<3,8>, <4,8>, <5,7>}
If you do the exercise, you find
|A^B| = |A|^|B|.

What you want to do is take a category of finite sets (representing the class of natural numbers) plus some F-object (where some notion of power F |-> F^2 exists) and have this be, in the bast case, "Cartesian closed", so that you can make sense of F^F, and in a way that passing from the category to a sort of cardinal arithmetic makes sense.

File: Screen Shot 2017-06-05 at 17.21.52.png (142KB, 682x458px) Image search: [Google]

142KB, 682x458px

>>8958257
Btw. my line of thinking is to proceed like e.g. algebraic geometry. You start out with something you understand (powers of functions here, algebriac varieties there), see that this doesn't suffice to do all the things you want to do (why can't we look at F^F, why can't we look at spaces with this and that nice feature), and then just force a structure that's large enough to have those features and also have the old one be embedded within it.
This approach seems to lie so close in your case, because exponentiation is a natural universal process that can be expressed in this language.

Whether you speak of turning gay and back here, or opening and closing yogurt cans is mere semantics. Just like the same equations may apply to particles in a gas and the traffic jam.

>>8958257
Okay fair enough, you did a good job.

>>8958211
Suppose there's a gayness rating, x, such that x>0 is straight, and x<0 is gay. Thus, if F=fag, we must have F<0; for arguments sake, lets say F=-1. This would explain why F^2=(-1)^2=1=not fag. Therefore, F^F=(-1)^(-1)=1/(-1)=-1=fag
I choose answer A