Set theory is one of the foundations of mathematics. It is now considered an independent mathematics branch with applications in topology, abstract algebra, and discrete mathematics. …

Think of a set as a box which contains (perhaps no) things. There is no repetition in a set, meaning each element must be unique. You could, for example, have variations on an …

Here we have a comprehensive collection of lessons on sets and set theory in math. We often deal with groups or collection of objects in real life, such a set of books, a group of students, a …

We begin by introducing the notion of the ordered pair. If a and b are sets, then the unordered pair {a, b} is a set whose elements are exactly a and b. The “order” in which a and b are put …

Example: students in this lecture. Small sets can be represented by showing all the members. Larger sets may be difficult to represent (infinite) so a notation must be used to specify the …

Sets are a useful vocabulary in many areas of mathematics. They provide a language for stating interesting results. For example, in analysis: “a monotone function from ‘ to ‘ is continuous …

Formal semantics is formulated in a language which is basically English (supposing that is the language of use) enhanced by numerous set-theoretic concepts. In this chapter, we examine …

Mar 31, 2025 · Introduction, Set Theory. Monday March 31. In our first lecture together, we'll discuss the big questions we will answer in CS103, then explore the finite and the infinite …

Thus, we need to understand some basic set theory as a prerequisite to understanding probability and statistics. De nition. A set is a collection of objects, where an \object" is a generic term that …

Set theory began with Cantor’s proof in 1874 that the natural numbers do not have the same cardinality as the real numbers. Cantor’s original motivation was to give a new proof of …

Venn diagrams are often used to discuss commonalities and differences between sets in the universal set. The universal set is everything within the rectangle encompassing the Venn …

For example, if we try to de ne the set of all sets, we will run into a problem called a paradox. M. Macauley (Clemson) Lecture 1.1: Basic set theory Discrete Mathematical Structures 2 / 14

Set theory is the field of mathematics that deals with the properties of sets that are independent of the things that make up the set. For example, a mathematician might be interested in knowing …

First order predicate calculus, universal and existential quantifiers. Basic logical inference (e.g., modus ponens, double-negation elimination). This document contains some exercises which …

A perceptual set is the tendency to interpret information based on past experiences, expectations, and emotions, shaping how we perceive and respond to stimuli. ... The Basic Idea Key Terms …

These notes cover introductory set theory. Starred sections below are op- tional. They discuss interesting mathematics connected to concepts covered in the course.