Empty set

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

Empty Set vs Set Containing Empty Set | Set Theory

What's the difference between the empty set and the set containing the empty set? We'll look at {} vs {{}} in today's set theory video lesson, discuss their cardinalities, and look at their power sets. As we'll see, the power set of the empty set is our friend { {} }! The river runs peacef

From playlist Set Theory

Power Set of the Power Set of the Power Set of the Empty Set | Set Theory

The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p

From playlist Set Theory

The Empty Set is a Subset of Every Set Proof

Please subscribe:) https://goo.gl/JQ8Nys The Empty Set is a Subset of Every Set Proof B-Roll - Islandesque by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) Source: http://incompetech.com/music/royalty-free/index.html

From playlist Set Theory

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 Sets and Set Notation

This video defines a set, special sets, and set notation.

From playlist Sets (Discrete Math)

What is the Power Set of the Empty Set? | Set Theory

What is the power set of the empty set? We will answer this question in today’s math lesson! We will write the empty set like so: { }. Recall that the power set of a set A is the set containing all subsets of A. So, for example, P({ 1 }) = { { }, { 1 } }. Also, recall that if the cardinali

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

The Empty Set or the Null Set , Intermediate Algebra , Lesson 27

This tutorial explains the simple concept of the empty set, otherwise known as the null set. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Intermediate Algebra

O'Reilly Webcast: Nullology: The Zen of Database

Nullology is the study of the empty set. Of course, sets crop up all over the place in the database world; but the question is--and it's a crucial one--what happens if the set under consideration happens to be empty? For example, a relation contains a set of tuples: what about the possibil

From playlist O'Reilly Webcasts

Find All Subsets of a Set (Example Problems) | Set Theory Exercises

How do you find all subsets of a given set? We go over eight subset example problems in today's lesson, including sets with the empty set, the empty set itself, sets with strange elements like the real numbers and the rationals, and more. We also briefly mention power sets, and the number

From playlist Set Theory

Proof: Cancellation Law for Cartesian Products | Set Theory

We prove the cancellation law for cartesian products. Suppose A, B, and C are sets with C nonempty. Then AxC=BxC. This is a straightforward set equality proof, we first have to consider the case where A is empty. Then, we'll suppose it is nonempty, and show A is a subset of B. It is the sa

From playlist Set Theory

SUBSETS AND POWER SETS - DISCRETE MATHEMATICS

Today we look at subsets and power sets. This includes the empty set, and the power set of the empty set. Support me on Patreon: http://bit.ly/2EUdAl3 Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.y

From playlist Discrete Math 1

Cartesian Products with Empty Sets | Set Theory, Cartesian Product of Sets, Empty Set

How do Cartesian products work with empty sets? Cartesian products are great and all, but we cannot eagerly dive into working with them without making sure we know how to deal with Cartesian products when empty sets are involved. We go over that in today's math lesson! Recall that the Car

From playlist Set Theory

Set Theory (Part 7): Natural Numbers and Induction

Please feel free to leave comments/questions on the video and practice problems below! In this video, I discuss the von Neumann construction of the natural numbers and relate the idea of natural numbers to inductive sets. The axiom of infinity is also introduced here as one of the ZFC axi

From playlist Set Theory by Mathoma

Every Set is an Element of its Power Set | Set Theory

Every set is an element of its own power set. This is because the power set of a set S, P(S), contains all subsets of S. By definition, every set is a subset of itself, and thus by definition of the power set of S, it must contain S. This is even true for the always-fun empty set! We discu

From playlist Set Theory

Empty Graph, Trivial Graph, and the Null Graph | Graph Theory

Whenever we talk about something that is defined by sets, it is important to consider the empty set and how it fits into the definition. In graph theory, empty sets in the definition of a particular graph can bring on three types/categories of graphs. The empty graphs, the trivial graph, a

From playlist Graph Theory