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| In ], '''hexation''' (or '''hyper-5''') is the next ] (infinite ] of arithmetic operations) after ] and before Heptation. It is defined as ] (repeated) pentation | |||
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| <big><math display="inline">a\uparrow\uparrow\uparrow\uparrow b = \underbrace{a\uparrow\uparrow\uparrow(a\uparrow\uparrow\uparrow(\cdots(a\uparrow\uparrow\uparrow a)))}_{b \text{ copies of } a} | |||
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| </math></big> | |||
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| }} | |||
| == Notation == | |||
| There is little consensus on the notation for hexation; as such, there are many different ways to write the operation. However, some are more used than others, and some have clear advantages or disadvantages compared to others. | |||
| * Pentation can be written as a ] as <math>a{b} | |||
| </math> | |||
| * In ], hexation can be represented as <math>a \uparrow \uparrow \uparrow \uparrow \uparrow b | |||
| </math> or <math>a {\uparrow}^5 {b} | |||
| </math> | |||
Revision as of 06:53, 6 January 2024
In mathematics, hexation (or hyper-5) is the next hyperoperation (infinite sequence of arithmetic operations) after Pentation and before Heptation. It is defined as iterated (repeated) pentation
Notation
There is little consensus on the notation for hexation; as such, there are many different ways to write the operation. However, some are more used than others, and some have clear advantages or disadvantages compared to others.
- Pentation can be written as a hyperoperation as
- In Knuth's up-arrow notation, hexation can be represented as or
or 