Tetration
repeated or iterated exponentiation
Tetration is the hyperoperation which comes after exponentiation.[1] means y exponentiated by itself, (x-1) times.[2][3][4] List of first 4 natural number hyperoperations, the inverse of tetration is the super root shown in the example
- Addition
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- n copies of 1 added to a.
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- Multiplication
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- n copies of a combined by addition.
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- Exponentiation
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- n copies of a combined by multiplication.
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- Tetration
- n copies of a combined by exponentiation, right-to-left.
The above example is read as "the nth tetration of a".
Examples
change1 1 (11) 1 (11) 1 (11) 2 4 (22) 16 (24) 65,536 (216) 3 27 (33) 7,625,597,484,987 (327) 1.258015 × 103,638,334,640,024 4 256 (44) 1.34078 ×10154 (4256) (8.1 × 10153 digits) 5 3,125 (55) 1.91101 × 102,184 (53,125) (1.3 × 102,184 digits) 6 46,656 (66) 2.65912 × 1036,305 (646,656) (2.1 × 1036,305 digits) 7 823,543 (77) 3.75982 × 10695,974 (7823,543) (3.2 × 10695,974 digits) 8 16,777,216 (88) 6.01452 × 1015,151,335 (5.4 × 1015,151,335 digits) 9 387,420,489 (99) 4.28125 × 10369,693,099 (4.1 × 10369,693,099 digits) 10 10,000,000,000 (1010) 1010,000,000,000 (1010,000,000,000 digits)
References
change- ↑ "Google Answers: addition, multiplication, exponentiation, then ???". Retrieved 2011-11-02.
- ↑ Daniel Geisler. "tetration.org". Tetration. Archived from the original on 2021-05-06. Retrieved 2011-11-02.
- ↑ "Power Tower - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2011-11-02.
- ↑ "The Fourth Operation". Retrieved 2019-09-11.