In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with... 43 KB (5,778 words) - 02:35, 3 April 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 (1,759 words) - 16:48, 21 March 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 |
introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc... 28 KB (3,390 words) - 19:42, 12 May 2024 |
magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation, or Conway chained... 8 KB (854 words) - 10:07, 3 February 2024 |
2=2\uparrow \uparrow \uparrow 2={\text{ }}...} up through any level of hyperoperation, here denoted in Knuth's up-arrow notation, all equivalent to 4. {\displaystyle... 30 KB (3,672 words) - 02:58, 27 April 2024 |
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 |
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 (6,780 words) - 10:55, 25 April 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) - 19:47, 18 March 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... 89 KB (9,912 words) - 17:24, 8 May 2024 |
first 20 of them are: Also see Fermat number, tetration and lower hyperoperations. All of these numbers end in 6. Starting with 16 the last two digits... 39 KB (3,882 words) - 13:54, 12 May 2024 |
source code. Common operator notation (for a more formal description) Hyperoperation Logical connective#Order of precedence Operator associativity Operator... 46 KB (4,367 words) - 22:09, 1 May 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... 18 KB (2,100 words) - 17:55, 17 February 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 (1,213 words) - 19:21, 9 April 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 (459 words) - 20:21, 2 June 2023 |
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 |
{\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}... 18 KB (2,453 words) - 01:55, 7 May 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... 23 KB (3,109 words) - 18:19, 21 April 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 (3,044 words) - 04:47, 5 April 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 |
{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 (1,578 words) - 06:22, 13 March 2024 |