Introduction to Set Theory

Authors

Karel Hrbacek, Thomas Jech

Year

1999

Abstract

A modern introduction to set theory, covering both naive and axiomatic approaches.

BibTeX

            @book{hrbacek1999introduction, title={Introduction to Set Theory}, author={Hrbacek, Karel and Jech, Thomas}, year={1999}, publisher={Marcel Dekker}}

Notations Used in This Paper

for Element Membership

A relation between an element and a set, indicating that the element belongs to the set

Typst: $x in A$

LaTeX: x \in A

Context: Fundamental set relation, first axiom of set theory

Referenced on page 12

Primary Definition

for Existential Quantification

A logical statement asserting that there exists at least one element satisfying a property

Typst: $exists x. P(x)$

LaTeX: \exists x. P(x)

Context: First-order logic introduction

Referenced on page 121

Primary Definition

for Set Intersection

The intersection of two sets A and B is the set of elements which are in both A and B

Typst: $A sect B$

LaTeX: A \cap B

Context: Basic set operations introduced in Chapter 2

Referenced on page 46

Primary Definition

for Set Union

The union of two sets A and B is the set of elements which are in A, in B, or in both

Typst: $A union B$

LaTeX: A \cup B

Context: Basic set operations introduced in Chapter 2

Referenced on page 45

Primary Definition

for Summation

The sum of a sequence of numbers, typically indexed over a range

Typst: $sum_(i=1)^n a_i$

LaTeX: \sum_{i=1}^{n} a_i

Context: Mathematical notation appendix

Referenced on page 302

for Universal Quantification

A logical statement asserting that a property holds for all elements in a domain

Typst: $forall x. P(x)$

LaTeX: \forall x. P(x)

Context: First-order logic introduction

Referenced on page 120

Primary Definition