Math 101 Introduction to Analysis 09 092017 The Extended Real Number System; Sequences
Extended real number system as a set; as an ordered set. Comment: all nonempty subsets have least upper bounds. Is not a field. Conventions. Definition of a sequence. Examples of sequences.
From playlist Course 6: Introduction to Analysis (Fall 2017)
The extended rational numbers in practice | Real numbers and limits Math Foundations 105
We review the extended rational numbers, which extend the rational numbers to all expressions of the form a/b, where a and b are integers---even b=0. Then we give some examples of how these strange beasts might prove useful in mathematics. But first we give one example of where they are un
From playlist Math Foundations
Different Types of Numbers on the number line, lesson 1 #shorts
Watch the full playlist: https://www.youtube.com/watch?v=kcxK3_sROZA&list=PL14bv5vXK2WWuODhGbpPQA0GamV5ohOVb&index=1 Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). This is the set of na
From playlist Celebrities Teach Math: The Number System
From playlist a. Numbers and Measurement
Reconsidering natural numbers and arithmetical expressions | Data structures Math Foundations 185
It is time to turn our gaze back to the true foundations of the subject: arithmetic with natural numbers. But now we know that the issue of "What exactly is a natural number?" is fraught with subtlety. We adopt a famous dictum of Errett Bishop, and start to make meaningful distinctions bet
From playlist Math Foundations
Ex: Write and Solve an Equation for Consecutive Natural Numbers with a Given Sum
This video explains how to set up and solve an equation involving consecutive natural numbers with a given sum. http://mathispower4u.com
From playlist Applications: Writing and Solving Equations
The realm of natural numbers | Data structures in Mathematics Math Foundations 155
Here we look at a somewhat unfamiliar aspect of arithmetic with natural numbers, motivated by operations with multisets, and ultimately forming a main ingredient for that theory. We look at natural numbers, together with 0, under three operations: addition, union and intersection. We will
From playlist Math Foundations
Identifying Sets of Real Numbers
This video provides several examples of identifying the sets a real number belongs to. Complete Video Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com
From playlist Number Sense - Properties of Real Numbers
Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018
Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
WHAT COMES AFTER EXPONENTS? Tetration examples and extensions | ND
This video about what comes after exponents and tetration (also known as hyper-4 or power tower math) was actually inspired by a comment left on the discussion page of my channel, so thanks Cullen! Anyhow, the goal of this video was to build up the idea of tetration from scratch and then i
From playlist The New CHALKboard
How to Take the Factorial of Any Number
In this video, I walk through the derivation of an extension of the factorial function that works for any number: fractional, irrational, and even complex! This turns out to be a very important function, known as the gamma function, which has many surprising connections, one of which I exp
From playlist Summer of Math Exposition 2 videos
Rings 12 Duality and injective modules
This lecture is part of an online course on rings and modules. We descibe some notions of duality for modules generalizing the dual of a vector space. We first discuss duality for free and projective modules, which is very siilar to the vector space case. Then we discuss duality for finit
From playlist Rings and modules
Analytic Continuation and the Zeta Function
Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co
From playlist Analytic Number Theory
Building an Infinite Bridge | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009. Tweet at us! @pbsinfinite F
From playlist An Infinite Playlist
Negatives numbers from anti msets | Math Foundations 231 | N J Wildberger
How do we set up negative numbers in this new arithmetic based purely on multisets or msets? The answer is surprising: we must adapt notions from 20th century particle physics: the idea of an antiparticle that shares many properties of a particle, but that mutually annihilates when in cont
From playlist Box Arithmetic
Tony Yue Yu - The Frobenius conjecture in dimension two
Abstract: We apply the counting of non-archimedean holomorphic curves to the construction of the mirror of log Calabi-Yau surfaces. In particular, we prove the Frobenius structure conjecture of Gross-Hacking-Keel in dimension two. This is joint work with Sean Keel.
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Natural Numbers can be either Even OR Odd - 2 Proofs & Partition of the Positive Integers
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Set Theory: https://www.youtube.com/watch?v=nvYqkhZFzyY Good mornin my sons and daugthers! Let us perform anice litle task today: Showing the video titles theorem
From playlist Number Theory
Live CEOing Ep 676: Language Design in Wolfram Language [Entity Raft]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design