Search results
Learning Objectives. After completing this section, you should be able to: Represent sets in a variety of ways. Represent well-defined sets and the empty set with proper set notation. Compute the cardinal value of a set. Differentiate between finite and infinite sets. Differentiate between equal and equivalent sets. Sets and Ways to Represent Them.
- 1.1: Basic Concepts of Set Theory
Intuitively, a set is a collection of objects with certain...
- 4.2: Basic Set Concepts
Sets can be described in a number of different ways: by...
- 1.1: Basic Concepts of Set Theory
Intuitively, a set is a collection of objects with certain properties. The objects in a set are called the elements or members of the set. We usually use uppercase letters to denote sets and lowercase letters to denote elements of sets. If \(a\) is an element of set \(A\), we write \(a \in A\).
23 cze 2024 · Sets can be described in a number of different ways: by roster notation, by set-builder notation, by interval notation, by graphing on a number line, and by Venn diagrams. Sets are typically designated with capital letters.
Basic set theory concepts and notation. At its most basic level, set theory describes the relationship between objects and whether they are elements (or members) of a given set. Sets are also objects, and thus can also be related to each other typically through use of various symbols and notations.
Basic concepts. The fundamental concepts of set theory are those of set, element, and membership. Based on these, cardinality, inclusion relations, set equality, and other operations are defined. Set. A set is a collection of well-defined and distinct objects. These objects can be concrete (numbers, letters) or abstract (ideas, concepts).
Set theory is a branch of mathematics that studies sets, which are essentially collections of objects. For example \ (\ {1,2,3\}\) is a set, and so is \ (\ {\heartsuit, \spadesuit\}\). Set theory is important mainly because it serves as a foundation for the rest of mathematics--it provides the axioms from which the rest of mathematics is built up.
A.1. Primitive Concepts. In mathematics, the notion of a set is a primitive notion. That is, we admit, as a starting point, the existence of certain objects (which we call sets), which we won’t define, but which we assume satisfy some basic properties, which we express as axioms.
