In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker (1949). The existence of Specker sequences has consequences for computable analysis. The fact that such sequences exist means that the collection of all computable real numbers does not satisfy the least upper bound principle of real analysis, even when considering only computable sequences. A common way to resolve this difficulty is to consider only sequences that are accompanied by a modulus of convergence; no Specker sequence has a computable modulus of convergence. More generally, a Specker sequence is called a recursive counterexample to the least upper bound principle, i.e. a construction that shows that this theorem is false when restricted to computable reals. The least upper bound principle has also been analyzed in the program of reverse mathematics, where the exact strength of this principle has been determined. In the terminology of that program, the least upper bound principle is equivalent to ACA0 over RCA0. In fact, the proof of the forward implication, i.e. that the least upper bound principle implies ACA0, is readily obtained from the textbook proof (see Simpson, 1999) of the non-computability of the supremum in the least upper bound principle. (Wikipedia).
The Thue-Morse Sequence (with visualizations)
In this video, we introduce the Prouhet-Thue-Morse sequence, which is a binary sequence. We discuss three methods to construct the sequence and then investigate some of the sequence's properties (including why it is the "fair sharing" sequence, the overlap-free property, its connection to
From playlist Fractals
Mirna Džamonja: Universal א2-Aronszajn trees
Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 14, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au
From playlist Logic and Foundations
Samson Abramsky - The sheaf-theoretic structure of contextuality and non-locality
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/AbramskySlidesToposesOnline.pdf Quantum mechanics implies a fundamentally non-classical picture of the physical worl
From playlist Toposes online
What is the definition of a geometric sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Proof that the Sequence {1/n} is a Cauchy Sequence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Sequence {1/n} is a Cauchy Sequence
From playlist Cauchy Sequences
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Ask Adam Savage: Creating Exaggerated Props for Story Purposes
Join this channel to support Tested and get access to perks, like asking Adam questions: https://www.youtube.com/channel/UCiDJtJKMICpb9B1qf7qjEOA/join In this livestream excerpt, Tested member BetterinWriting wrote to Adam, "I'm quite fascinated by the quality of exaggeration that theatre
From playlist Adam Savage's Live Streams
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Introduction to Sequences (Discrete Math)
This video introduces sequences for a discrete math class. mathispower4u.com
From playlist Sequences (Discrete Math)
Sequence Definition and Examples Welcome to our sequence adventure! In this video, I give some basic examples of sequences, and in the remainder of the playlist we'll discover beautiful properties of sequences and their limits. Enjoy! Check out my Sequences Playlist: https://www.youtube.
From playlist Sequences
What is the recursive formula and how do we use it
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Heather Macbeth - Algorithm and abstraction in formal mathematics - IPAM at UCLA
Recorded 17 February 2023. Heather Macbeth of Fordham University at Lincoln Center presents "Algorithm and abstraction in formal mathematics" at IPAM's Machine Assisted Proofs Workshop. Abstract: Paradoxically, the formalized version of a proof is often both more abstract and more computat
From playlist 2023 Machine Assisted Proofs Workshop
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Ruby Hoedown 2008 - Lightning Talk: TATFT - Test All the F***in Time by: Bryan Liles
Lightning Talk: TATFT - Test All the F***in Time by: Bryan Liles Help us caption & translate this video! http://amara.org/v/G1S1/
From playlist Ruby Hoedown 2008
Bell's Theorem: The Quantum Venn Diagram Paradox
Featuring 3Blue1Brown Watch the 2nd video on 3Blue1Brown here: https://www.youtube.com/watch?v=MzRCDLre1b4 Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ This video is about Bell's Theorem, one o
From playlist Guest appearances on other channels
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We dicuss the axiom of chice, and sketch why it is independent of the other axioms of set theory. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50f
From playlist Zermelo Fraenkel axioms
Burlington Ruby Conf 2013 Building Ambitious APIs with Ruby by Dan Gebhardt
With the advent of native and single page web apps, APIs are more important than ever. An application's API often must serve the needs of its own front end(s) as well as any third party applications and scripts that integrate with it. It should be flexible, yet follow strong conventions to
From playlist Burlington Ruby Conf 2013
GRCon19 - A decade of gr-specest -- Free Spectral Estimation! by Martin Braun
A decade of gr-specest -- Free Spectral Estimation! by Martin Braun 10 years ago, the Communications Engineering Lab (CEL) of KIT, Germany, published an out-of-tree module for GNU Radio: The spectral estimation toolbox (gr-specest). Today, it’s still around and works even with the latest
From playlist GRCon 2019
What is subscript notation and how does it relate to functions
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences