Jan 10, 2025 · Set theory is a mathematical discipline focused on the study of well-defined collections of distinct objects, known as sets, and their relationships and operations.

Discrete Mathematics - Sets - German mathematician G. Cantor introduced the concept of sets. He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or description.

Jul 30, 2024 · Discover the different types of sets in discrete mathematics. Learn about empty sets, finite sets, infinite sets, and more with clear definitions and examples.

A set is a collection of objects (without repetitions). To describe a set, either list all its elements explicitly, or use a descriptive method. Intervals are sets of real numbers. The elements in a set can be any type of object, including sets. We can even have a set containing dissimilar elements.

For us, a set will simply be an unordered collection of objects. Two examples: we could consider the set of all actors who have played The Doctor on Doctor Who, or the set of natural numbers between 1 and 10 inclusive.

Jun 30, 2024 · Discrete mathematical structures include objects with distinct values like graphs, integers, logic-based statements, etc. In this tutorial, we have covered all the topics of Discrete Mathematics for computer science like set theory, recurrence …

CS 441 Discrete mathematics for CS M. Hauskrecht Set operations Definition: Let A and B be sets. The union of A and B, denoted by A B, is the set that contains those elements that are either in A or in B, or in both. • Alternate: A B = { x | x A x B }. • Example: • A = {1,2,3,6} B = { 2,4,6,9} • A B = { 1,2,3,4,6,9 } U A B

Set A is a subset of Set B if and only if every element in Set A is also in Set B. In symbols: A ⊂ B x ∈ A → x ∈ B. We designate these notations for some special sets of numbers: N = the set of natural numbers, Z = the set of integers, Q = the set of …

May 9, 2023 · The following are the types of sets in discrete mathematics: 1. Singleton Set. If a set contains only one element it is called to be a singleton set. Hence the set given by {1}, {0}, {a} are all consisting of only one element and therefore are singleton sets. 2. Finite Set.

The set of natural numbers \(\mathbb{N}\) are the “whole numbers”: \(0, 1, 2, 3, \ldots\). The set of integers \(\mathbb{Z}\) are the whole numbers and their negatives: \(\ldots, -2, -1, 0, 1, 2, \ldots\). The set of real numbers \(\mathbb{R}\) are “all” the numbers, including fractions, decimals, and irrational numbers like \(\pi\).