Just as the phrase “what the entire fuck” implies the existence of fractional fucks, the phrase “what the absolute fuck” implies the existence of both positive and negative fucks (or else there would be no need for an absolute value operation). Taken together with the phrase “what the actual fuck” (which implies the existence of imaginary fucks), we may thus conclude that fuckery is isomorphic with the complex field.
Technically, we can only conclude that “a fuck” is an element of some norm space over a field containing fractional values; the space being isomorphic to ℂ is a substantially stronger claim.
If anyone ever said “what the rational fuck” we would have a stronger basis for ℂ, as that would imply some irrational fucks. We could then generously assume completeness and thus a Banach space that is at least a subset of ℂ. However, no mention has also been made of whether this is a bounded space (”what the finite fuck?” could be taken as implication of infinite fucks on at least some axis), so there are many unexplored areas of research in fuck-topology.
I think we’ve been overlooking the fact that we don’t even know that fuckery has ring structure – without needing to multiply fucks (though fucks are often thought to lead to multiplying), fuck-space doesn’t need to be over a field.
It could just be a module over some ring containing the integers but not contained by the reals (giving us our negative and “non-actual” fucks), where “a fuck” is a multiple of some generator of the module (giving fractional fucks).
“Entire” fuck may also hint at Lang’s usage, referring to an integral domain as the base ring, but this seems superfluous.
It has been brought to my attention that we’ve been ignoring ignoring “what the literal fuck”. This suggests that fucks exist not only within a module structure as you suggest, but also could be represented as words in some logical formal language (with the “literal” fucks being the atomic fucks and their negations).
This, of course, raises the question of what relationship if any connects the vector space/module operations with any rules which might describe the formal rules of “fuck logic”.
In any group of people outside of your normal circle, you may find various permutations of all of these fucks. I had a co worker that would always use “ what in the blue fuck” implying the existence of color to fuck, or the ability of fucks to register on a visual scale.
I’ve been known to use “ what the bionic fuck” and once heard a woman at work say “ what a French fuck”. Debra Morgan (hbo series Dexter) once said “ what the fillet of fuck”, which has always made me laugh.
