Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. Originally published by Van Nostrand in 1960, it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of ZFC set theory (except the Axiom of Foundation), and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: there are no discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals. Instead, it tries to be intelligible to someone who has never thought about set theory before. Halmos later stated that it was the fastest book he wrote, taking about six months, and that the book "wrote itself". (Wikipedia).
The Most Famous Book on Set Theory
In this video I will show you what is considered to be perhaps the most influential book ever written on Set Theory. The book is called Set Theory and it was written by Felix Hausdorff. Another wonderful book is Naive Set Theory by Paul Halmos. We will look at both books and I will explain
From playlist Book Reviews
Basic Methods: We introduce basic notions from naive set theory, including sets, elements, and subsets. We give examples of showing two sets are equal by mutual inclusion. Then we define the power set and note Russell's paradox.
From playlist Math Major Basics
We give some basic definitions and notions associated with sets. In particular, we describe sets via the "roster method", via a verbal description, and with set-builder notation. We also give an example of proving the equality of two sets. Please Subscribe: https://www.youtube.com/michael
From playlist Proof Writing
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to Set Theory (Discrete Mathematics)
Introduction to Set Theory (Discrete Mathematics) This is a basic introduction to set theory starting from the very beginning. This is typically found near the beginning of a discrete mathematics course in college or at the beginning of other advanced mathematics courses. ***************
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Why is the Empty Set a Subset of Every Set? | Set Theory, Subsets, Subset Definition
The empty set is a very cool and important part of set theory in mathematics. The empty set contains no elements and is denoted { } or with the empty set symbol ∅. As a result of the empty set having no elements is that it is a subset of every set. But why is that? We go over that in this
From playlist Set Theory
An Introduction to Sets (Set Theory)
What is a set in math? What are elements? What is cardinality? What are subsets? In this video we will answer all of those questions. We will pinpoint the definition of sets in math, talk about elements, explain what cardinality is, and what a subset is. I hope you find this video helpful,
From playlist Set Theory
Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets
Here is a method for completely listing the subsets of a given set using tree diagrams. It's a handy way to make sure you don't miss any subsets when trying to find them. It's not super efficient, but it is reliable! The process is pretty simple, we begin with the empty set, and then branc
From playlist Set Theory
Buried Math Book Treasure at the Beach
In this video we go looking around the beach for a long lost forgotten math book. What better place to do a book review than the actual beach:) We end up finding a book, which is very famous and well written. The book is called Naive Set Theory and it is written by Paul R. Halmos. This
From playlist Cool Math Stuff
The Problem of Perception (John Searle)
John Searle discusses here the nature of perception and some of the main positions in the history of philosophy, as well as some of the problems that arise for each type of view. This is a version of something that I put together awhile ago and that was originally uploaded to the previous
From playlist Philosophy of Mind
Naive Set Theory by Paul Halmos #shorts
Naive Set Theory by Paul Halmos #shorts Full Review Here: https://youtu.be/9EjT047Pv1w This is the book on amazon: https://amzn.to/34LVtd0 (note this is my affiliate link) Book Review #shorts: https://www.youtube.com/playlist?list=PLO1y6V1SXjjPqMhU21NyGnwVnlF0UIheP Full Book Reviews: h
From playlist Book Reviews #shorts
Naive homology versus Suslin homology - Fabien Morel
Fabien Morel March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
You should know what Impredicativity is.
In this video I discuss the concept of predicativity, impredicativity and vicious circles. The text for the video is found in https://gist.github.com/Nikolaj-K/aae1f4bd582e60e6b7e5b5431fee054c
From playlist Logic
Learn Mathematics from START to FINISH
This video shows how anyone can start learning mathematics , and progress through the subject in a logical order. There really is no finishing point but this will get you through all of the basic undergraduate mathematics from start to "finish". I also included some graduate topics. Here
From playlist Book Reviews
John Searle Interview on Perception & Philosophy of Mind
One of America’s most prominent philosophers says his field has been tilting at windmills for nearly 400 years. Representationalism (or indirect realism)---the idea that we don’t directly perceive external objects in the world, but only our own inner mental images or representations of obj
From playlist Philosophy of Mind
What is a set: Basics of sets and quantifiers in math | Intro to Math Structures VS1.2
I'm sort of going to tell you what a set is while avoiding the ZFC axioms. This video has some exercises dispersed through it and goes through the basics of sets in math. In particular we'll go through basic notation, the union, intersection, set difference, complement, and symmetric diff
From playlist The CHALKboard 2022
Seven Math Books for Seven Math Subjects You can Learn Without Calculus
I go over seven books for seven different math subjects that in theory anyone can learn without calculus. These are the books. Graph Theory by Gould https://amzn.to/2Ge92c2 An Introduction to Abstract Mathematics by Bond and Keane https://amzn.to/3ncIAQv Naive Set Theory by Paul Halmos
From playlist Book Reviews
How to Identify the Elements of a Set | Set Theory
Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times
From playlist Set Theory