In mathematical logic, in particular in model theory and nonstandard analysis, an internal set is a set that is a member of a model. The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the real numbers R, and the properties of a larger field denoted *R called the hyperreal numbers. The field *R includes, in particular, infinitesimal ("infinitely small") numbers, providing a rigorous mathematical justification for their use. Roughly speaking, the idea is to express analysis over R in a suitable language of mathematical logic, and then point out that this language applies equally well to *R. This turns out to be possible because at the set-theoretic level, the propositions in such a language are interpreted to apply only to internal sets rather than to all sets (note that the term "language" is used in a loose sense in the above). Edward Nelson's internal set theory is an axiomatic approach to nonstandard analysis (see also Palmgren at constructive nonstandard analysis). Conventional infinitary accounts of nonstandard analysis also use the concept of internal sets. (Wikipedia).
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)
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
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
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
Determine Sets Given Using Set Notation (Ex 2)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)
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
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
Proof: Menger's Theorem | Graph Theory, Connectivity
We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see
From playlist Graph Theory
Intro to Menger's Theorem | Graph Theory, Connectivity
Menger's theorem tells us that for any two nonadjacent vertices, u and v, in a graph G, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths in G. The Proof of Menger's Theorem: https://youtu.be/2rbbq-Mk-YE Remember that
From playlist Graph Theory
Inernal Languages for Higher Toposes - Michael Shulman
Michael Shulman University of California, San Diego; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Definable equivariant retractions onto skeleta in (...) - M. Hils - Workshop 3 - CEB T1 2018
Martin Hils (Münster) / 28.03.2018 Definable equivariant retractions onto skeleta in non-archimedean geometry For a quasi-projective variety V over a non-archimedean valued field, Hrushovski and Loeser recently introduced a pro-definable space Vb, the stable completion of V , which is a
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
RubyConf Mini 2022: Start a Ruby Internship by Chelsea Kaufman and Adam Cuppy
Starting an internship doesn’t have to reduce your team's progress. On the contrary, a quality internship can benefit interns and senior folks. And, it doesn't take much to set up and start. We've done over 100! You’ll use our established blueprint to draft a successful internship program
From playlist RubyConf 2022: Mini and Houston
The Curious Case of ShellExecute
Open Analysis Live! Why can't you hook and suspend processes created via ShellExecute? We take a look at the internals for ShellExecute and what happens when that API is used to create a new process. ----- OALABS DISCORD https://discord.gg/6h5Bh5AMDU OALABS PATREON https://www.patreon.c
From playlist Open Analysis Live!
Pullbacks under the logarithmic derivative
From playlist Workshop on Model Theory, Differential/Difference Algebra, and Applications
Cohomology in difference algebra and geometry We view difference algebra as the study of algebraic objects in the topos of difference sets, i.e., as `ordinary algebra’ in a new universe. The methods of topos theory and categorical logic enable us to develop difference homological algebra,
From playlist DART X
Tom Leinster : The categorical origins of entropy
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
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
When Does Migration Law Discriminate Against Women?
It is possible to identify gendered disadvantage at almost every point in a migrant woman’s journey, physical and legal, from country of origin to country of destination, from admission to naturalization. The presentation by Dr. Catherine Briddick draws on this literature to examine whethe
From playlist Refugee Program Seminars