Mathematical notation | Large numbers
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc.Various notations have been used to represent hyperoperations. One such notation is .Knuth's up-arrow notation is an alternative notation. It is obtained by replacing in the square bracket notation by arrows.For example: * the single arrow represents exponentiation (iterated multiplication) * the double arrow represents tetration (iterated exponentiation) * the triple arrow represents pentation (iterated tetration) The general definition of the up-arrow notation is as follows (for ): Here, stands for n arrows, so for example (Wikipedia).
Raising a scientific number to the third power
👉 Learn how to multiply numbers written in scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is
From playlist Scientific Notation
Examples: Writing a Number in Decimal Notation When Given in Scientific Notation
This video provided two examples of writing a number in decimal notation that is given in scientific notation. Complete Video List: http://www.mathispower4u.com
From playlist Scientific Notation
Dividing two numbers in scientific notation then rewriting answer in scientific notation
👉 Learn how to divide numbers written in scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is t
From playlist Scientific Notation
Examples: Write a Number in Scientific Notation
This video provides two examples of rewriting a number in scientific notation. Complete Video List: http://www.mathispower4u.com
From playlist Scientific Notation
Converting a number to scientific notation
👉 Learn how to convert numbers to scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the numb
From playlist Scientific Notation
Rewrite a number from scientific notation when it is smaller that
👉 Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu
From playlist How to Convert Scientific Notation to a Number
What is the definition of scientific notation
👉 Learn about scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the number of digits up to t
From playlist Scientific Notation | Learn About
How Big is Graham's Number? (feat Ron Graham)
See our other Graham's Number videos: http://bit.ly/G_Number More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ The magnitude of Graham's Number is difficult to fathom - Ron Graham himself attempts to explain. WHAT IS the number: http://youtu
From playlist Big Numbers on Numberphile
Rick Sommer - Knuth’s Up-Arrow into the Transfinite & Beyond! - G4G14 Apr 2022
Famous for its world-record status, Graham’s number has captured the imagination of recreational mathematicians ever since being introduced by Martin Gardner in Mathematical Recreations in 1977. Knuth’s up-arrow notation builds on a nifty recursion that is used to define Graham’s number, a
From playlist G4G14 Videos
The Largest Numbers Ever Discovered // The Bizarre World of Googology
Check out Brilliant â–º https://brilliant.org/TreforBazett/ Learn math more effectively for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this video on unfathomably large numbers. Check out my MATH MERCH line in colla
From playlist Cool Math Series
Stanford Lecture: Don Knuth—"The Associative Law, or the Anatomy of Rotations in Binary Trees"
First Annual Christmas Lecture November 30, 1993 Professor Knuth is the Professor Emeritus at Stanford University. Dr. Knuth's classic programming texts include his seminal work The Art of Computer Programming, Volumes 1-3, widely considered to be among the best scientific writings of the
From playlist Donald Knuth Lectures
MegaFavNumbers: Conway's Chained Arrow Notation
This video is for the #MegaFavNumbers project. So far, almost 200 people have submitted their favorite numbers over 1 million. I am choosing a number that is bigger than Graham's number. This can be done with a mathematical notation called "Conway's Chained Arrow Notation". This notation
From playlist MegaFavNumbers
Multiplying in scientific notation with negative exponents
👉 Learn how to multiply numbers written in scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is
From playlist Scientific Notation
Stanford Lecture: Donald Knuth - "Bayesian trees and BDDs" (2011)
December 8th, 2011 Professor Donald Knuth's 17th annual Christmas Tree Lecture. Knuth explains how to apply elementary BDD technology so that the probability of such events (and many others) can be computed in polynomial time. Learn more: http://scpd.stanford.edu/knuth/index.jsp
From playlist Donald Knuth Lectures
#MegaFavNumbers The Digits of Graham's Number
Hello everyone, welcome to the channel. I hope you enjoy the videos I make! And plz forgive me. I am actually portuguese so I hope you understand what I say hehe Huge thanks to Matt Parker: https://www.youtube.com/user/standupmaths and to James Grime: https://www.youtube.com/c/singi
From playlist MegaFavNumbers
Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016)
Computer Musings 2016 Donald Knuth's 23rd Annual Christmas Tree Lecture: "Hamiltonian Paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its steps.
From playlist Donald Knuth Lectures
Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016) (360 Degrees)
Computer Musings 2016 Donald Knuth's Christmas Tree Lecture (360 degrees): "Hamiltonian paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its step
From playlist Donald Knuth Lectures
Find the quotient between two numbers by converting to scientific notation
👉 Learn how to divide numbers written in scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is t
From playlist Scientific Notation
Rewriting a number into scientific notation with a positive power
👉 Learn how to convert numbers to scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the numb
From playlist Scientific Notation
Stanford Lecture: "Aha" Sessions - Problem 4 - Distributed stability Wrap Up
March 12, 1985 Notes from these problem sessions were published as A Programming and Problem-Solving Seminar, Stanford Technical Report No. STAN-CS-85-1055. (http://www-cs-faculty.stanford.edu/~knuth/papers/cs1055.pdf) Professor Knuth is the Professor Emeritus at Stanford University. Dr.
From playlist Donald Knuth Lectures