In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with...
43 KB (5,786 words) - 22:35, 15 October 2024
In mathematics, pentation (or hyper-5) is the fifth hyperoperation. Pentation is defined to be repeated tetration, similarly to how tetration is repeated...
9 KB (1,746 words) - 16:20, 12 August 2024
Hyperstructure (redirect from Hyperoperation (group theory))
called a hyperoperation. The largest classes of the hyperstructures are the ones called H v {\displaystyle Hv} – structures. A hyperoperation ( ⋆ ) {\displaystyle...
2 KB (301 words) - 12:29, 28 November 2023
Successor operations are also known as zeration in the context of a zeroth hyperoperation: H0(a, b) = 1 + b. In this context, the extension of zeration is addition...
3 KB (389 words) - 13:27, 27 March 2024
introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc...
28 KB (3,400 words) - 16:13, 23 September 2024
exponentiation. It would be read as "the nth tetration of a". It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben...
54 KB (6,474 words) - 16:45, 14 October 2024
Iterating tetration leads to another operation, and so on, a concept named hyperoperation. This sequence of operations is expressed by the Ackermann function...
104 KB (13,637 words) - 16:01, 16 October 2024
Steinhaus' mega lies between 10[4]257 and 10[4]258 (where a[n]b is hyperoperation). Mathematics: Moser's number, "2 in a mega-gon" in Steinhaus–Moser...
90 KB (9,971 words) - 13:44, 13 October 2024
magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation, or Conway chained...
7 KB (772 words) - 13:40, 8 October 2024
Hindi Hypercube, the n-dimensional analogue of a square and a cube Hyperoperation, an arithmetic operation beyond exponentiation Hyperplane, a subspace...
2 KB (246 words) - 12:13, 12 July 2024
common in mathematics. The upward-pointing arrow is now used to signify hyperoperations in Knuth's up-arrow notation. It is often seen in caret notation to...
11 KB (1,166 words) - 16:28, 16 September 2024
first 20 of them are: Also see Fermat number, tetration and lower hyperoperations. All of these numbers over 4 end with the digit 6. Starting with 16...
39 KB (3,970 words) - 15:03, 9 October 2024
{\displaystyle f^{4}(n)=f(f(f(f(n))))} . Expressed in terms of the family of hyperoperations H 0 , H 1 , H 2 , ⋯ {\displaystyle {\text{H}}_{0},{\text{H}}_{1},{\text{H}}_{2}...
19 KB (2,474 words) - 19:46, 29 September 2024
and hyperbolic growth lie more classes of growth behavior, like the hyperoperations beginning at tetration, and A ( n , n ) {\displaystyle A(n,n)} , the...
24 KB (3,250 words) - 00:03, 9 October 2024
\uparrow 2)} , or as the pentation, 2 [ 5 ] 3 {\displaystyle 2[5]3} (hyperoperation notation). 65536 is a superperfect number – a number such that σ(σ(n)) = 2n...
5 KB (634 words) - 00:13, 6 October 2024
completely stable. Common operator notation (for a more formal description) Hyperoperation Logical connective#Order of precedence Operator associativity Operator...
48 KB (4,547 words) - 04:00, 12 October 2024
{\displaystyle \omega :X^{n}\rightarrow {\mathcal {P}}(X)} . Finitary relation Hyperoperation Infix notation Operator Order of operations "Algebraic operation - Encyclopedia...
11 KB (1,211 words) - 05:14, 10 October 2024
extends these basic operations in a way that can be compared to the hyperoperations: φ ( m , n , 3 ) = m [ 4 ] ( n + 1 ) φ ( m , n , p ) ⪆ m [ p + 1 ]...
51 KB (6,786 words) - 20:41, 15 October 2024
introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the naming convention now used for these operations...
6 KB (458 words) - 07:26, 4 August 2024
x0 := x0 + 1 END; LOOP x2 DO x0 := x0 + 1 END Multiplication is the hyperoperation function H 2 {\displaystyle \operatorname {H_{2}} } H 2 ( x 1 , x...
17 KB (2,096 words) - 09:55, 16 October 2024
n ) = 2 [ m ] ( n + 3 ) − 3 {\displaystyle A(m,n)=2[m](n+3)-3} in hyperoperation) hence 2 → n → m = A ( m + 2 , n − 3 ) + 3 {\displaystyle 2\to n\to...
15 KB (3,068 words) - 14:26, 9 July 2024
hierarchy coincide with those of the Grzegorczyk hierarchy: (using hyperoperation) f0(n) = n + 1 = 2[1]n − 1 f1(n) = f0n(n) = n + n = 2n = 2[2]n f2(n)...
13 KB (1,561 words) - 11:16, 24 February 2024
{E}}^{1}\subsetneq {\mathcal {E}}^{2}\subsetneq \cdots } because the hyperoperation H n {\displaystyle H_{n}} is in E n {\displaystyle {\mathcal {E}}^{n}}...
10 KB (1,631 words) - 21:55, 16 August 2024
a fixed number of recursions, notably Knuth's up-arrow notation and hyperoperation notation. Mathematical notation Mark Cutler, Physical Infinity, 2004...
3 KB (498 words) - 16:54, 21 January 2024