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
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
This video introduces the basic vocabulary used in set theory. http://mathispower4u.wordpress.com/
From playlist Sets
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
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
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
What are equal sets? Subsets in math is an important concept for understanding the definition of equality in set theory. In this video we define equality in sets, which is fairly simple. One of the properties of equal sets is that if sets A and B are equal, then A is a subset of B and B is
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
Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Commutative algebra 42 Projective modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the relation between locally free things (vector bundles) and projective things. In commutative algebra and differe
From playlist Commutative algebra
The TRUTH about TENSORS, Part 2: Free Bugaloo
In this video we write down the definition of free modules in terms of a universal property, and prove that it exists.
From playlist The TRUTH about TENSORS
The Digamma Function at Integer Values!
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Digamma intro: https://youtu.be/kjK9
From playlist Number Theory
CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 2
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)
LC001.03 - Clifford algebras and matrix factorisations
A brief introduction to Clifford algebras, their universal property, how to construct a Clifford algebra from the Hessian of a quadratic form, and how modules over that Clifford algebra determine matrix factorisations. This video is a recording made in a virtual world (https://www.roblox.
From playlist Metauni
Commutative algebra 41 Locally free modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define locally free modules and explain that they are analogs of vector bundles in geometry. We give some examples of local
From playlist Commutative algebra
Math subsets are an important concept to understand. So what is the subset definition in math? What is a subset? We go over that part of set theory in this video as well as some details on the empty set and its subset properties. Enjoy! I hope you find this video helpful, and be sure to a
From playlist Set Theory
Lecture 18. Rank is well-defined
From playlist Abstract Algebra 2
How a sheep I met in 6th grade helped me get to my first International Math Olympiad #SoME2
This is my submission for the 2022 Summer of Math Exposition #SOME #Summerofmathexposition #competitivemath #SoME2 TIMESTAMPS: 00:00 Intro 00:14 How you get to the International Math Olympiad 00:44 What I needed to solve 01:15 The problem 02:30 First idea 03:54 Playing with the problem
From playlist Summer of Math Exposition 2 videos
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
