In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with...

In mathematics, pentation (or hyper-5) is the fifth hyperoperation. Pentation is defined to be repeated tetration, similarly to how tetration is repeated...

called a hyperoperation. The largest classes of the hyperstructures are the ones called H v {\displaystyle Hv} – structures. A hyperoperation ( ⋆ ) {\displaystyle...

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...

introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc...

magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation, or Conway chained...

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...

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...

Iterating tetration leads to another operation, and so on, a concept named hyperoperation. This sequence of operations is expressed by the Ackermann function...

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...

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...

Hindi Hypercube, the n-dimensional analogue of a square and a cube Hyperoperation, an arithmetic operation beyond exponentiation Hyperplane, a subspace...

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...

{\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}...

\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...

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 ]...

and hyperbolic growth lie more classes of growth behavior, like the hyperoperations beginning at tetration, and A ( n , n ) {\displaystyle A(n,n)} , the...

{\displaystyle \omega :X^{n}\rightarrow {\mathcal {P}}(X)} . Finitary relation Hyperoperation Infix notation Operator Order of operations "Algebraic operation - Encyclopedia...

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...

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...

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...

source code. Common operator notation (for a more formal description) Hyperoperation Logical connective#Order of precedence Operator associativity Operator...

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)...

a fixed number of recursions, notably Knuth's up-arrow notation and hyperoperation notation. Mathematical notation Mark Cutler, Physical Infinity, 2004...

{E}}^{1}\subsetneq {\mathcal {E}}^{2}\subsetneq \cdots } because the hyperoperation H n {\displaystyle H_{n}} is in E n {\displaystyle {\mathcal {E}}^{n}}...