What is the difference between Set, and Class in object oriented languages?

Question

What is the difference between Set in set theory, and Class in object oriented languages?

Answer 1

There are debates about the definition, but, for elementary work, a set is just a collection of things, which are called its "members". So $\{3, \pi, \text{Jupiter}\}$ is a set whose members are two numbers and a planet. The members of a set do not all have to be the same kinds of things, and they do not need to have any relationship to each other.

In object-oriented programming, a class provides a "blueprint" or "template" for objects of a similar type, that have some common set of properties and methods. Specific objects that follow the blueprint are called "instances" of the class.

In programming, the closest thing to a set is a C# ArrayList or a Python tuple. These are both collections whose members can be anything you like. For example

ArrayList a = { 3, System.Math.Pi, "hello" };

is a perfectly legal definition of an ArrayList whose members are two numbers and a string.

But sets and ArrayList-like collections still have some large differences. ArrayLists are finite, and sets are often infinite. Also, the elements of an ArrayList have a specific order, and elements of a set do not. In common programming languages, I can't think of a data structure that represents an unordered collection.

In short, sets and classes have very little in common, so asking how they are different is a somewhat odd question.

Answer 2

In set theory, there are things called equivalence relations which can be used to glob things that are alike into sets called equivalence classes. I think this is where the class idea comes from programming. The objects created by a class in programming all have the same structure and so in some sense they are equivalent!

A class in programming is a "program-code-template" so I don't know what type of "thing" a template even is. This question is way too hard.