# Category: Large numbers

Knuth's up-arrow notation
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 op
Buchholz hydra
In mathematical logic, the Buchholz hydra game is a hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rap
1,000,000
One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione (milione in modern Italian), fro
Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though and the left-exponent xb are common. Under th
Billion
A billion is a number with two distinct definitions: * 1,000,000,000, i.e. one thousand million, or 109 (ten to the ninth power), as defined on the short scale. This is now the meaning in all English
Trillion
Trillion is a number with two distinct definitions: * 1,000,000,000,000, i.e. one million million, or 1012 (ten to the twelfth power), as defined on the short scale. This is now the meaning in both A
The Sand Reckoner
The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains o
Large numbers
Large numbers are numbers significantly larger than those typically used in everyday life (for instance in simple counting or in monetary transactions), appearing frequently in fields such as mathemat
Hyperoperation
In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n
Steinhaus–Moser notation
In mathematics, Steinhaus–Moser notation is a notation for expressing certain large numbers. It is an extension (devised by Leo Moser) of Hugo Steinhaus's polygon notation.
Pentation
In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration, just as tetration is iterated exponentiation. It
Names of large numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but t
Skewes's number
In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number for which where π is the prime-
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 f
Conway chained arrow notation
Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by r
Indefinite and fictitious numbers
Many languages have words expressing indefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary
1,000,000,000
1,000,000,000 (one billion, short scale; one thousand million or one milliard, one yard, long scale) is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" c
Cutler's bar notation
In mathematics, Cutler's bar notation is a notation system for large numbers, introduced by Mark Cutler in 2004. The idea is based on iterated exponentiation in much the same way that exponentiation i
Goodstein's theorem
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Kirby an
History of large numbers
Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture. Two interesting points in using large numbers are the c