Rather than everyone yelling things like “But I need to know when, given some particular set, a relation can be defined upon that set which splits the set up into disjoint subsets whose union is the original set! Perhaps we should consider things in each subset as equal to each other and maybe call this a partition!”.
Post sets along with some binary relation that partitions the set here. Then it’s open season to find homomorphisms among and between any set that ends up here.
Equivalence will be judged on:
1)Reflexivity: a ~ a
2)Symmetry: if a ~ b then b ~ a
3)Transitivity: if a ~ b and b ~ c then a ~ c.
All these can be rated on a binary scale where 0 equals “fuck no this doesn’t hold” and 1 equals “oh hell goddamn yes this requirement holds”.
Thread A Is-Derived-From Thread B when the existence of thread A can be attributed to a theme or statement which originated in Thread B. So, for example. The Equivalence Relation ThreadIs-Derived-FromThe Equivalence Thread
I give this a 0/0/0
The statement Thread AIs-Derived-FromThread A is not always true (and, in fact, may always be false pending some further axioms relating to Thread Creation)
Due the way time works if Thread AIs-Derived-FromThread B then the reverse probably can’t hold.
If Thread AIs-Derived-FromThread B and Thread BIs-Derived-FromThread C then is it always the case that Thread AIs-Derived-FromThread C? I think the answer is no. If, for example, this thread were to become derailed into a discussion of pancakes and someone were to create a thread polling people on prefered pancake types, could it be said that the pancake thread Is-Derived-From the original equivalence thread? That would be insanity!