OP, I need the definition for × and <,> too
× is the cartesian product and = {x, {x,y}} is the ordered pair of x and y. (i.e., if x is in X and y is in Y, then is the corresponding element of the cartesian product X × Y). hope this helps
Oh wow, I should know that… Thanks
What does type() mean here?
it’s the “order type” of a well ordering on a set. so, given a set X with a total ordering R, type(X,R) is the unique ordinal isomorphic to (X,R)
what’s with the square at the end? isn’t that usually for proofs?
yeah but sometimes when the textbook authors are feeling particularly mischievous they’ll just put them in random places. and sometimes they’ll even skip the proofs but keep the square.
Give it up for op actually out here answering questions like a real live teacher.
× is the cartesian product I think, no clue what the other thing is tho
Is this from Principia Mathematica or smth?
This looks like classical ordinal set theory in relatively modern notation. I’d guess that Principia Mathematica uses batshit notation compared to this but I haven’t read it.
This is giving me PTSD flashbacks from Number Theory at uni. What a fascinating mindfuck.
oh god number theory… the things they make you do in that class…
statements dreamed up by the utterly deranged
QED.
Mathematicians write the most insane shit you’ve ever seen in your life then they’re just like □ peace out
If you wrote the equivalent of this in software I think linus torvalds himself would personally show up to destroy your pc.
Nah, formulas like that are basically the assembly code for logic.
Oh no, there are xis!!!
https://www.change.org/p/the-entire-multiverse-ban-xi-from-the-greek-alphabet
Im sorry, but the capital form alone justifies its existence.
