Tetration

From Simple English Wikipedia, the free encyclopedia

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

  1. Addition
    n copies of 1 added to a.
  2. Multiplication
    n copies of a combined by addition.
  3. Exponentiation
    n copies of a combined by multiplication.
  4. Tetration
n copies of a combined by exponentiation, right-to-left.

The above example is read as "the nth tetration of a".

Examples[change | change source]

1 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 | change source]

  1. "Google Answers: addition, multiplication, exponentiation, then ???". Answers.google.com. Retrieved 2011-11-02.
  2. Daniel Geisler. "tetration.org". Tetration. Archived from the original on 2021-05-06. Retrieved 2011-11-02.
  3. "Power Tower - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2011-11-02.
  4. "The Fourth Operation". Retrieved 2019-09-11.