Set Theory

Back to Discrete Mathematics
Arjit Sharma
01 Min

Set Theory might sound academic, but it’s everywhere in development - from deduplicating data to writing cleaner algorithms or SQL queries.

What is a Set?

A set is a well-defined, unordered collection of distinct elements. Think of it as a way to group things without duplicates.

Notation

  • Tabular form:

    A = {apple, banana, orange}

  • Set-builder form:

    B = {x | x is a prime number < 10} → {2, 3, 5, 7}

Types of Set

Finite Set

const permissions = new Set(['read', 'write', 'delete'])

Infinite Set

function naturalNumbers() {
    let n = 1;
    while (true) n++;
}

Empty Set

const emptySet = new Set()

Common Set Operations

set operations

1. Union (∪) - Combine all unique elements

A = {1, 2, 3}
B = {3, 4}
A U B = {1, 2, 3, 4, 5}

2. Intersection (∩) - Common elements

A = {1, 2, 3}
B = {3, 4}
A ∩ B = {3}

3. Difference (−) - Elements in A but not in B

A = {1, 2, 3}
B = {3, 4}
A-B = {1, 2}

How Developers Use Sets

De-duplication

Sets help remove duplicates from lists like tags, cache, or user inputs.

const cache = new Set();
cache.add('user123');
cache.add('user123'); // Duplicate ignored

Databases

Set theory powers common SQL operations like UNION, INTERSECT, and EXCEPT.

SELECT id FROM active_users
UNION
SELECT id FROM premium_users;

Role-Based Access

const adminPermissions = new Set(['read', 'write', 'delete']);

function hasPermission(roleSet, action) {
    return roleSet.has(action);
}

hasPermission(adminPermissions, 'delete'); // true

Conclusion

Set Theory helps developers write cleaner, more efficient code. Whether it’s handling unique values, writing SQL queries sets are a fundamental tool worth mastering.

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