Why doesn't java.util.Set have get(int index)?

Because sets have no ordering. Some implementations do (particularly those implementing the java.util.SortedSet interface), but that is not a general property of sets.

If you're trying to use sets this way, you should consider using a list instead.

Just adding one point that was not mentioned in mmyers' answer.

If I know I want the first item, I can use set.iterator().next(), but otherwise it seems I have to cast to an Array to retrieve an item at a specific index?

What are the appropriate ways of retrieving data from a set? (other than using an iterator)

You should also familiarise yourself with the SortedSet interface (whose most common implementation is TreeSet).

A SortedSet is a Set (i.e. elements are unique) that is kept ordered by the natural ordering of the elements or using some Comparator. You can easily access the first and last items using first() and last() methods. A SortedSet comes in handy every once in a while, when you need to keep your collection both duplicate-free and ordered in a certain way.

Edit: If you need a Set whose elements are kept in insertion-order (much like a List), take a look at LinkedHashSet.

This kind of leads to the question when you should use a set and when you should use a list. Usually, the advice goes:

1. If you need ordered data, use a List
2. If you need unique data, use a Set
3. If you need both, use either: a SortedSet (for data ordered by comparator) or an OrderedSet/UniqueList (for data ordered by insertion). Unfortunately the Java API does not yet have OrderedSet/UniqueList.

A fourth case that appears often is that you need neither. In this case you see some programmers go with lists and some with sets. Personally I find it very harmful to see set as a list without ordering - because it is really a whole other beast. Unless you need stuff like set uniqueness or set equality, always favor lists.

I'm not sure if anybody has spelled it out exactly this way, but you need to understand the following:

There is no "first" element in a set.

Because, as others have said, sets have no ordering. A set is a mathematical concept that specifically does not include ordering.

Of course, your computer can't really keep a list of stuff that's not ordered in memory. It has to have some ordering. Internally it's an array or a linked list or something. But you don't really know what it is, and it doesn't really have a first element; the element that comes out "first" comes out that way by chance, and might not be first next time. Even if you took steps to "guarantee" a particular first element, it's still coming out by chance, because you just happened to get it right for one particular implementation of a Set; a different implementation might not work that way with what you did. And, in fact, you may not know the implementation you're using as well as you think you do.

People run into this ALL. THE. TIME. with RDBMS systems and don't understand. An RDBMS query returns a set of records. This is the same type of set from mathematics: an unordered collection of items, only in this case the items are records. An RDBMS query result has no guaranteed order at all unless you use the ORDER BY clause, but all the time people assume it does and then trip themselves up some day when the shape of their data or code changes slightly and triggers the query optimizer to work a different way and suddenly the results don't come out in the order they expect. These are typically the people who didn't pay attention in database class (or when reading the documentation or tutorials) when it was explained to them, up front, that query results do not have a guaranteed ordering.

some data structures are missing from the standard java collections.

Bag (like set but can contain elements multiple times)

UniqueList (ordered list, can contain each element only once)

seems you would need a uniquelist in this case

if you need flexible data structures, you might be interested in Google Collections

That's true, element in Set are not ordered, by definition of the Set Collection. So they can't be access by an index.

But why don't we have a get(object) method, not by providing the index as parameter, but an object that is equal to the one we are looking for? By this way, we can access the data of the element inside the Set, just by knowing its attributes used by the equal method.

If you are going to do lots of random accesses by index in a set, you can get an array view of its elements:

Object[] arrayView = mySet.toArray();
//do whatever you need with arrayView[i]

There are two main drawbacks though:

1. It's not memory efficient, as an array for the whole set needs to be created.
2. If the set is modified, the view becomes obsolete.

That is because Set only guarantees uniqueness, but says nothing about the optimal access or usage patterns. Ie, a Set can be a List or a Map, each of which have very different retrieval characteristics.

The only reason I can think of for using a numerical index in a set would be for iteration. For that, use

for(A a : set) { 
   visit(a); 
}

Set is an interface and some of its implementation classes are HashSet, TreeSet and LinkedHashSet. It uses HashMap under the hood to store values. Because HashMap does not preserve the order, it is not possible to get value by index.

You now must be thinking how Set is using HashMap since HashMap stores a key, value pair but the Set does not. valid question. when you add an element in Set, internally, it maintains a HashMap where the key is the element you want to enter in Set and the value is the dummy constant. Below is an internal implementation of add function. Hence, all the keys in the HashMap will have the same constant value.

// Dummy value to associate with an Object in the backing Map
private static final Object PRESENT = new Object();

public boolean add(E e) {
    return map.put(e, PRESENT)==null;
}

Because the Set stores unique elements in random locations and Internally It uses multiple data structures. i.e. Array, linked list, a tree with hashing.

link https://en.wikipedia.org/wiki/Set_(abstract_data_type)