Questions
can a set contain itself?
No
do infinite sets have domains?
domains are properties of quantified proofs, not sets
(but there is another word "domain" we'll see later)
how do I get something out of a set?
no
also: can't talk about a specific element except by value
{1} vs {{1}} -- what's the difference?
we create a set of sets to talk about sets
can we simplify {{1}} to {1}?
No. We also cannot simplify {1} to 1
can sets have variables?
not really?
incomplete:
my number is x + 3
my set is {x}
why are sets so important to logic?
they let us talk about more than one thing
are sets with several types inside useful?
not very often
how are sets useful in coding?
math sets: let us prove things about code
data structure "sets": take algorithms
are sets more useful than lists?
math does have lists, it has tuples
but no, they are differently useful (really yes)
in code: lists seem to be winning
do sets in programming follow logic set properties?
mostly