and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg-Wainer hierarchy) is an ordinal-indexed...

the set of natural numbers, {0, 1, ...}). It contrasts with the fast-growing hierarchy. Let μ be a large countable ordinal such that a fundamental sequence...

{\displaystyle i>1} . The Grzegorczyk hierarchy can be extended to transfinite ordinals. Such extensions define a fast-growing hierarchy. To do this, the generating...

called Hardy functions. It is related to the fast-growing hierarchy and slow-growing hierarchy. The Hardy hierarchy was introduced by Stanley S. Wainer in 1972...

Porto & Matos 1980. Odifreddi 1999, p. 298. "The Ackermann hierarchy vs. the fast growing hierarchy". StackExchange. Indentation according to the off-side...

General Hospital, in Barrow-in-Furness, England Fast-growing hierarchy, a method to describe fast-growing functions. This disambiguation page lists articles...

Fast-growing hierarchy These notations are essentially functions of integer variables, which increase very rapidly with those integers. Ever-faster-increasing...

10^{15}}+3}} Even faster-growing functions can be categorized using an ordinal analysis called the fast-growing hierarchy. The fast-growing hierarchy uses successive...

the reliance on fundamental sequences. The fast-growing hierarchy, Hardy hierarchy, and slow-growing hierarchy of functions are all defined via a chosen...

Ackermann function and Graham's number bounds see fast-growing hierarchy#Functions in fast-growing hierarchies.) Goodstein's theorem can be used to construct...

the exponent. In the fast-growing hierarchy, 2n is exactly equal to f 1 n ( 1 ) {\displaystyle f_{1}^{n}(1)} . In the Hardy hierarchy, 2n is exactly equal...

function is faster than the standard fast-growing hierarchy, as F i ( x ) {\displaystyle F_{i}(x)} alone grows at the rate of the fast-growing hierarchy, and...

chained arrow notation Encyclopedic size comparisons on Wikipedia Fast-growing hierarchy Indian numbering system Infinity Large numbers List of numbers Mathematical...

A bounding volume hierarchy (BVH) is a tree structure on a set of geometric objects. All geometric objects, which form the leaf nodes of the tree, are...

[1] 2 Wikifunctions has a hyperoperation function. Large numbers Fast-growing hierarchy Sequences similar to the hyperoperation sequence have historically...

can be divided into an infinite hierarchy of increasingly large complexity levels, according to the fast-growing hierarchy. The 𝐅 0 {\displaystyle {\text{𝐅}}_{0}}...

are shared downward within the buyer hierarchy so the team can consider lower cost production options. The fast fashion industry incorporates a variety...

top-level hierarchy refers to the hierarchy defined by the prefix before the first dot. The most commonly known hierarchies are the Usenet hierarchies. So for...

For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate...

{\displaystyle 2^{O(k)}} , but the definition admits functions that grow even faster. This is essential for a large part of the early history of this class...

learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract...

determined by birth. A hierarchical system wherein generally the Brahmins were at the head of the hierarchy, but this hierarchy was disputed in some cases...

Non-finicky omnivores make the best candidates. Growth rate – The animal must grow fast enough to be economically feasible. Elephant farmers, for example, would...

their kypes continue to grow. This fast growing skeletal tissue fuses with the dense dentary, becoming a permanent, growing kype. Many male trout (e...

of the entire memory system (generally, the memory hierarchy follows the access time with the fast CPU registers at the top and the slow hard drive at...

amounts of cache for any given amount of chip area. Most CPUs have a hierarchy of multiple cache levels (L1, L2, often L3, and rarely even L4), with...

his concept of a hierarchy of needs in a paper in 1943. He argued that as people's basic survival needs are met, so their desire to grow in mental and emotional...

other hand, the loss of detail as abstraction of information ascends a hierarchical organization can lead to distortion that results in bad decision-making...

by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined...

sugarcane. Twice each week and on the first Sunday of every month, the Bobos fast. Almost all songs and tributes within the community end with the phrase "Holy...