If function composition is chaotic, then set intersection is certainly not lawful.
Not being commutative is pretty chaotic
Set theory is relatively lawful.
Counter point, no lawful theory shell let 5 ∪ 7 type check.
I mean… Ideal theory of rings? (Smth like (5) ∪ (7))
I feel yields different result than 5 ∪ 7 in the classical set theoretical encoding… I believe 5 ∪ 7 = 7 in the standard encoding of set theory. Because ∪ is the join operation in the natural number lattice (every total order give a lattice structure), yet the lattice structure in ideals of natural number ring is different: the join is LCM and the meet is GCD.
I guess my objection is that the ∪ and ∩ in the set theoretical encoding is rather trivial: the lattice structure in a total order is not terribly informative. Yet the standard encoding of natrual number in category theory (the category generated by one arrow on one object) is slightly more interesting, as composition encodes addition, which is arguably the most interesting opration on natrual numbers.
That being said arguing about encoding of natrual number is not the most informative discussion. but I feel set theory in general is very low level, yet people usually think in more algebraic and high level way, which aligns more closely with category theory.
Totally, set theory is deep dark magic and tbh set theorists kinda scare me. Like they’ll gleefully introduce incredibly complicated objects with very little intuition about them
Namely: lawful, true, chaotic, good, neutral and evil.You know the top left one. They teach that in schools.
I mean, yeah, I studied computer science. Presumably, I’ve been taught the majority of these at some point. I just absolutely fucking hate mathematical notation.
Due to your comment, I’m guessing, top-left is multiplication then, even though I was also taught in school to use × for multiplication.
Top-center might be logical AND? Top-right might be function composition? Center-left and center-right might be ranges, unless those dots indicate multiplication, then no fucking clue. Bottom left is set intersection. And one of these circles or crosses is probably the Cartesian product.So, I mean, I do know some of this shit. In truth, I was just deriding mathematical notation with that meme, because well, “Set” is the only actual word in all that mathematical notation… 😵💫
yeah, top-left is regular multiplication. Top-center actjally is the so-called alternating product (basically the correct way of defining the cross product).
Top-right is supposed to be the operation in a gtoup.
There’s no explicit cartesian product here but the middle one is the tensor product. The tensor prodict of sets (in so far as that statement makes sense) is the cartesian product.
:)