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| #REDIRECT ] | |||
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| '''Hexation''' is the operation of repeated ], just as ] is the operation of repeated ] and is a ]. Like pentation and tetration, it has little real-world applications, and has few applications even in mathematics. It is non-commutative, and therefore has two inverse functions, which might be named the '''hexa-root''' and the '''hexa-logarithm''' (analogous to the two inverse functions for exponentiation: ] function and ]). Hexation is not ]. | |||
| The word "Hexation" was coined by ] from the roots ] (six) and ]. It is part of his general naming scheme for ]. | |||
| Hexation can be written in ] as <math>a \uarr \uarr \uarr \uarr b</math> or <math>a \uarr^{4} b</math>. | |||
| ==Extension== | |||
| It is not known how to extend hexation to ] or non-integer values. | |||
| ==Selected values== | |||
| As its base operation (pentation) has not been extended to non-integer heights, hexation <math>a \uarr^{4} b</math> is currently only defined for integer values of ''a'' and ''b'' where ''a'' > 0 and ''b'' ≥ 0. Like all other ] of order 3 (]) and higher, pentation has the following trivial cases (identities) which holds for all values of a and b within its domain: | |||
| *<math>1 \uarr^{4} b = 1</math> | |||
| *<math>a \uarr^{4} 1 = a</math> | |||
| Other than the trivial cases shown above, hexation generates extremely large numbers very quickly such that there is only one fnon-trivial case that produces numbers that can be written in conventional notation, as illustrated below: | |||
| *<math> 2 \uarr^{4} 2 = 4</math> | |||
| This is the reason why hexation is not normally used in mathematics: the numbers it produces are so vast that they have little use. | |||
| {{Hyperoperations}} | |||
Revision as of 07:54, 15 November 2009
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