Hierarchy of functions | Large numbers | Computability theory | Proof theory

Fast-growing hierarchy

In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy) is an ordinal-indexed family of rapidly increasing functions fα: N → N (where N is the set of natural numbers {0, 1, ...}, and α ranges up to some large countable ordinal). A primary example is the Wainer hierarchy, or Löb–Wainer hierarchy, which is an extension to all α < ε0. Such hierarchies provide a natural way to classify computable functions according to rate-of-growth and computational complexity. (Wikipedia).

Video thumbnail

Limit levels + self-similarity in successor-limit hierarchy | Data structures Math Foundations 184

The successor - limit hierarchy exhibits interesting kinds of self-similarity, along the lines of fractals. One manifestation of this appears when we look at the levels of the limits in the sequence. In this video we go further in the sequence to really dizzying heights, probably obtaini

From playlist Math Foundations

Video thumbnail

The Hierarchy of Operations

An exploration of the Hierarchy of Operations for the SoME1 competition by 3Blue1Brown.

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Hierarchical Clustering 5: summary

[http://bit.ly/s-link] Summary of the lecture.

From playlist Hierarchical Clustering

Video thumbnail

Biological Classification of Hierarchy || #Shorts || Deveeka Ma'am || Infinity Learn Class 9&10

Biological classification is the scientific method of organizing and categorizing living organisms based on shared characteristics. This system allows us to study the diversity of life on Earth and understand how different species are related to one another. The hierarchy of biological cla

From playlist Shorts

Video thumbnail

The 5 Kingdoms in Classification | Evolution | Biology | FuseSchool

The 5 Kingdoms in Classification | Evolution | Biology | FuseSchool The classification system organises species into domain, kingdom, phylum, class, order, family, genus and finally species. ‘Kingdom’ is the second highest rank below the rank of domain in this sequence of classification

From playlist BIOLOGY: Evolution

Video thumbnail

The Hierarchy of Life

Paul Andersen explains how biology is ordered in the hierarchy of life. He first of all describes how emergent properties appear as you move to more inclusive systems. The then describes life at the following levels; atom, molecule, macromolecule, organelle, cell, tissue, organ, organ sy

From playlist Biology

Video thumbnail

The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100

►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857 ►Check out MAPLE LEARN for your browser to make beautiful graphs and much more: https://www.maplesoft.com/products/learn/?p=TC-9857 ►

From playlist Calculus II (Integration Methods, Series, Parametric/Polar, Vectors) **Full Course**

Video thumbnail

Growth of Functions at Infinity

Calculus: We use L'Hopital's Rule to compare the growth at infinity of x^{1/n} and ln(x).

From playlist Calculus Pt 5: Advanced Integration Techniques

Video thumbnail

Maslow's Hierarchy of Needs Is Incomplete — There’s a Final, Forgotten Stage | Best of '16

Maslow's Hierarchy of Needs Is Incomplete — There’s a Final, Forgotten Stage New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge -----------------------------------------------------------------------------

From playlist Best Videos | Big Think

Video thumbnail

GoGaRuCo 2012 - High Performance Ruby

High Performance Ruby by: Charles Nutter

From playlist gogaruco 2012

Video thumbnail

War Machines Are Developing Faster Than Our Ability to Regulate Them | Big Think

War Machines Are Developing Faster Than Our Ability to Regulate Them Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Wher

From playlist Best Videos | Big Think

Video thumbnail

Stimson Lectures: Anne-Marie Slaughter, “Power, Policy, and Leadership in a Networked World”

Anne-Marie Slaughter, president and CEO of New America, and the Bert G. Kerstetter ’66 University Professor Emerita of Politics and International Affairs at Princeton University, gave a series of three talks in November on “The Strategy of Connection” for the Henry L. Stimson Lectures on W

From playlist The MacMillan Center

Video thumbnail

Formal Organizations: Crash Course Sociology #17

Today we are exploring the world of formal organizations. We’ll go back to the historical process of rationalization and its impact on organizations in the form of bureaucracy and then discuss how organizations change in response to their organizational environment. We will also go over th

From playlist Sociology

Video thumbnail

Reach Your Escape Velocity

(May 4, 2011) Geoffrey Moore, author and venture partner at Mohr Davidow Ventures, talks about strategies and advice to help companies that are stuck in a sales and development rut escape and move ahead of the competition. Moore's approach centers on power, rather than performance, to over

From playlist Lecture Collection | Entrepreneurial Thought Leaders Seminar

Video thumbnail

Dynamic Graph Algorithms and Their Implementation

Abstract: While many algorithmic graph problems have been solved for static graphs, graphs that are used as models in various applications often change dynamically and, thus, require algorithms that can adapt quickly to the deletion and insertion of edges. I will start with providing an ov

From playlist SIAG-ACDA Online Seminar Series

Video thumbnail

16.2.1 Even More Memory Hierarchy

MIT 6.004 Computation Structures, Spring 2017 Instructor: Chris Terman View the complete course: https://ocw.mit.edu/6-004S17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62WVs95MNq3dQBqY2vGOtQ2 16.2.1 Even More Memory Hierarchy License: Creative Commons BY-NC-SA Mo

From playlist MIT 6.004 Computation Structures, Spring 2017

Video thumbnail

Stack Data Structure - Algorithm

This is an explanation of the dynamic data structure known as a stack. It includes an explanation of how a stack works, along with pseudocode for implementing the push and pop operations with a static array variable.

From playlist Data Structures

Related pages

Ackermann function | Primitive recursive function | Slow-growing hierarchy | Graham's number | Bachmann–Howard ordinal | Feferman–Schütte ordinal | Limit ordinal | Analytical hierarchy | Computable function | Veblen function | Ordinal number | Proof theory | Large countable ordinal | Grzegorczyk hierarchy | Hyperoperation | Computability theory | Hardy hierarchy | Computational complexity theory | Goodstein's theorem | Kruskal's tree theorem