tetration means the arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times. It carries an Arena rating of 1365, earned across 25 head-to-head judged battles.
Among words judged in Lexicurio's Arena, tetration ranks #137 of 17,124 for Most Sublime Words, #1,601 of 17,149 for Most Exacting Words, #2,065 of 17,151 for The Improbable, #3,206 of 17,132 for Most Betrayed by Its Sound.
tetration is pronounced /tɛˈtɹeɪʃn̩/.
Why “tetration” is a great word
The arithmetic operation of repeated exponentiation, where a base number is raised to the power of itself a specified number of times. From tetra- (prefix meaning 'four') and iteration, as it is the fourth operation in the sequence after addition, multiplication, and exponentiation; coined in the 20th century by the English mathematician Reuben Goodstein. Unlike exponentiation, which is a single ascent from base to power, or iteration, a general term for any repetitive process, tetration is the precise, formal successor in the hierarchy of hyper-operations. It builds recursive power-towers where numbers ascend into inconceivable magnitudes: 2 tetrated to 4 is a vertical stack of four twos; 3 tetrated to 3 is a ladder of 7.6 trillion rungs; it is the mind's quiet vertigo upon realizing such explosive growth lay latent in the simplest integers all along.
Etymology
From tetra- (prefix meaning ‘four’) + (itera)tion, from the fact that tetration is in fourth place after addition, multiplication, and exponentiation. The word was coined by the English mathematician Reuben Goodstein (1912–1985).
noun
- The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times.
Definitions & examples from Wiktionary (CC BY-SA 3.0).
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