Set theory is a branch of logic which studies collections of distinct elements, called sets. Topics include set operations (such as intersection and union), relations and mappings between sets, and the ordering of elements of sets (often through binary predicates).
I've had trouble understanding joins in sql and came upon this image which I think might help me. The problem is that I don't fully understand it. For example, the join in the top right corner of the image, which colors the full B circle red and…
I'm trying to determine how many different ways I can remove a group of values from a sequence, leaving the original sequence in order (stable), and making sure to remove only 1 instance value each from the original sequence. For example, if I had…
Assuming that you want to implement set theory concepts such as element, set, collection and relation in Java: How would you represent the empty set ∅?
Do I mislead myself, if I think of the NULL concept as it is used by the three-valued logic of…
I have two collections a and b. I would like to compute the set of items in either a or b, but not in both (a logical exclusive or). With LINQ, I can come up with this:
IEnumerable Delta(IEnumerable a, IEnumerable b)
{
return…
Given the input array
[a,b,c,d,e]
and a 'join' function (a,b) => (a+b)
my code returns the following array of arrays, containing each possible variation obtained by applying the join function to various pairs of elements whilst maintaining the…
I have two NSArrays A and B that share some common elements, e.g.
A: 1,2,3,4,5
B: 4,5,6,7
I would like to create a new NSArray consisting of the contents common between the two NSArrays joined with the contents of the second NSArray while…
I'm designing a class library for discrete mathematics, and I can't think of a way to implement an infinite set.
What I have so far is: I have an abstract base class, Set, which implements the interface ISet. For finite sets, I derive a class…
I'm drawing a blank, or as some would say, having a senior moment. I know there’s a formal definition and a name for the concept where a db operation (stored procedure) that runs in a database will yield the same results if run repeatedly.
It's…
I am trying to implement a list difference routine in prolog.
For some reason the following fails:
difference(Xs,Ys,D) :- difference(Xs,Ys,[],D).
difference([],_,A,D) :- D is A, !.
difference([X|Xs],Ys,A,D) :-
not(member(X,Ys)),
A1 is [X|A],
…
I am a bit confused about the name Intersection Types in Typescript.
In set theory, intersection would imply that only properties that are common to both types would be available in the intersection of the two.
In fact, that is how Typescript…
How can I describe in Coq that one set Y is a subset of another set X?
I tested the following:
Definition subset (Y X:Set) : Prop :=
forall y:Y, y:X.
, trying to express that if an element y is in Y, then y is in X. But this generates type errors…
Recently I came across a situation where set theory and set math fit what I was doing to the letter (granted there was an easier way to accomplish what I needed - i.e. LINQ - but I didn't think of that at the time). However I didn't know of any…
Assume we have trillions of sets stored somewhere. The domain for each of these sets is the same. It is also finite and discrete. So each set may be stored as a bit field (eg: 0000100111...) of a relatively short length (eg: 1024). That is, bit X in…
I have N integers, for example 3, 1, 4, 5, 2, 8, 7. There may be some duplicates. I want to divide this sequence into contiguous subsequences such that we can form from them non-decreasing sequence. How to calculate minimal number of cuts? For the…
