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#REDIRECT ] |
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{{Redirect category shell| |
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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 ]. |
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{{R from subtopic}} |
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}} |
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The word "Hexation" was coined by ] from the roots ] (six) and ]. It is part of his general naming scheme for ]. |
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Hexation can be written in ] as <math>a \uarr \uarr \uarr \uarr b</math> or <math>a \uarr^{4} b</math>. |
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==Extension== |
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It is not known how to extend hexation to ] or non-integer values. |
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==Selected values== |
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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: |
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*<math>1 \uarr^{4} b = 1</math> |
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*<math>a \uarr^{4} 1 = a</math> |
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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: |
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*<math> 2 \uarr^{4} 2 = 4</math> |
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This is the reason why hexation is not normally used in mathematics: the numbers it produces are so vast that they have little use. |
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{{Hyperoperations}} |
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