Well, we can start with a quick review of an equivalence relation. Dredging back into the snaqmolithic era, when gargantuan munchmodons masticated the world over, there was a subset of a union of two sets, say Ferd and Nurleen. Now this little subset was a fine subset, the envy of many precursors to fast foods, multinational corporations posing as mythical demiurges such as Monsanto Claus. And this subset had several unique qualities. They are:
Symmetric: For each x in Ferd or Nurleen, (x,x) was in this subset
Reflexive: For each (x,y) in the subset, (y,x) was in the subset.
Transitive: If (x,y) was in the subset and (y,z) was in the subset, then (x,z) was in the subset.
Any subset that admitted an equivalence relation was known as a setoid.
As the years passed and the gods were busy supposedly formulating the poodle and man was getting conned by woman into getting a job so that the poodle could be clipped, the little setoids evolved, emerging from their chrysalis, stretching their leathery bat wings and rambling on about carburators, ink pots, cardboard cutout sundowns and politics. Lo and behold, before they knew it, they had developed into congruences.
Now some of these congruences were furry, some smooth and some shaved. It's unclear to Science actually if they were shaved, waxed or hewn with a dull floppy disk, but it is known that they had stubble. And they too wondered how Rusty knew that Iceman braided his ass hairs. But that's another question for science. What the consortium of snow freaks really wants to know is:
1) Did he get any in France. If so, from how many?
2) Why didn't he post that picture here?
3) If he doesn't post that picture, somebody else will.
And so the congruences grew, changed, became political prisoners of some just cause like Religion, Hate, Greed and other offspring of Good Intentions. Then some loser logicians got a hold of them and through germnetic energizing, pooted out a helical fuzzy set, known for didactic orgasms of a singular wetness, posing as Good Seance and seducing supposedly pious financiers who should have known better. Thus was born the Prickly Incongruence.
And so the lowly furry equivalence relation grew into a furry congruence and through unnatural intercourse with humans, became prickly incongruences.
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