# Set vs Class: Exploring the Differences

• MHB
• highmath
In summary, sets can be viewed as classes, but not all classes are sets. Sets can be constructed using axioms in modern set theory, while classes that cannot be constructed this way are known as proper classes. An example of a proper class is the class of all sets.
highmath
What the differences between set and class?

highmath said:
What the differences between set and class?
Hi highmath,

Each set can be viewed as a class, but the converse is not true. You can have sets of sets, but not necessarily sets of classes.

A class is basically any collection you can think of; this was the approach used by Cantor in his initial theory (the naive set theory). However, it soon became apparent that attempting to build a set theory on that basis led to contradictions; one of these contradictions is Russel's paradox.

To solve that problem, modern set theory uses an axiomatic method: there is a set of axioms (the standard system is called ZFC) that define a limited set of operations that can be used to construct sets. The collection of objects that satisfy a property is a class, but, unless you can construct it using the axioms of the theory, you cannot assume that it is a set; in particular, you cannot use it as a member of a set.

A class that is not a set is called a proper class. For example, the class of all sets is a proper class: there is no set of all sets.

## What is the difference between a set and a class?

A set is a collection of distinct objects, while a class is a collection of objects that share similar characteristics or properties. Sets are typically used for mathematical operations, while classes are used in object-oriented programming.

## Can a set contain duplicate elements?

No, a set cannot contain duplicate elements. Each element in a set must be unique.

## How are sets and classes represented in computer programming languages?

Sets are typically represented using curly brackets, while classes are represented using class declarations with properties and methods.

## What is the purpose of using sets and classes?

Sets are commonly used for storing and performing mathematical operations on data, while classes are used for creating objects with specific attributes and behaviors in object-oriented programming.

## Can a class be considered a type of set?

No, a class and a set are distinct concepts. While both involve collections of objects, they serve different purposes and have different properties and operations associated with them.

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