Can a set have duplicate elements?

Question

I have been asked a question that is a little ambiguous for my coursework.

The array of strings is regarded as a set, i.e. unordered.

I\'m not

Answer 1

From Wikipedia in Set (Mathematics)

A set is a collection of well defined and distinct objects.

Perhaps the confusion derives from the fact that a set does not depend on the way its elements are displayed. A set remains the same if its elements are allegedly repeated or rearranged.

As such, the programming languages I know would not put an element into a set if the element already belongs to it, or they would replace it if it already exists, but would never allow a duplication.

Programming Language Examples

Let me offer a few examples in different programming languages.

In Python

A set in Python is defined as "an unordered collection of unique elements". And if you declare a set like a = {1,2,2,3,4} it will only add 2 once to the set.

If you do print(a) the output will be {1,2,3,4}.

Haskell

In Haskell the insert operation of sets is defined as: "[...] if the set already contains an element equal to the given value, it is replaced with the new value."

As such, if you do this: let a = fromList([1,2,2,3,4]), if you print a to the main ouput it would render [1,2,3,4].

Java

In Java sets are defined as: "a collection that contains no duplicate elements.". Its add operation is defined as: "adds the specified element to this set if it is not already present [...] If this set already contains the element, the call leaves the set unchanged".

Set myInts = new HashSet<>(asList(1,2,2,3,4));
System.out.println(myInts);

This code, as in the other examples, would ouput [1,2,3,4].