Dictionary

tetration en · NOUN

Pronunciation

• /tɛˈtɹeɪʃən/ (General-American)
• /tɛˈtɹeɪʃn̩/ (Received-Pronunciation)
• (Southern-England) audio

Etymology

PIE word *kʷetwóres 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).

Meanings

1. (uncountable, usually) 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.
   • Tetration is usually symbolized with a number drawn to the upper left of another number, as opposed to the upper right used for exponents. Let's look at an example: what is 2 tetrated to the 4th? We would draw this as a 2 with a little 4 to the upper left side: ⁴². This is equivalent to 2#123;2#123;2² 2016, Erik Seligman, “Simple Surprises”, in Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics, New York, N.Y.: Apress, Springer Science+Business Media, →DOI, →ISBN, page 11:
   • Repeated exponentiation—called tetration—is so rare that a shorthand for it is hardly worth the trouble, appealing only to research mathematicians. Most professional engineers and scientists never encounter tetration, and the shorthand for it is seldom taught anywhere but in mathematics departments. But it doesn't stop there, and for the almost-unheard-of "multiple tetration" there is yet a stronger cousin operation, waiting in the wings. 1993, Alexander Humez, Nicholas Humez, Joseph Maguire, “One”, in Zero to Lazy Eight: The Romance of Numbers, New York, N.Y.: Touchstone, Simon & Schuster, →ISBN, page 39:
   • You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below. ⁴²#61;2#123;(2#123;(#123;2²#125;)#125;)#125; #61;2#123;(#123;2⁴#125;)#125; #61;2#123;16#125; #61;64,536 1982 May, Rudy Rucker, “All the Numbers”, in Infinity and the Mind: The Science and Philosophy of the Infinite, Boston, Mass.; Stuttgart, Baden-Württemberg: Birkhäuser, →ISBN, page 69:

Forms

Coordinates

√ = (root extraction; degree) · multiplication · × ×... = (multiplication, factorization; factor) · hexation · × = (multiplication, factorization; multiplier) · + = (addition, summation) · successor · addition · + +... = (addition, summation) · Or sometimes (numerator) / (denominator) = (quotient) · pentation · log(base) = (logarithmization) · = (exponentiation; base) · ÷ = (division; dividend) · succession · exponentiation · − = (subtraction)

Deriveds

tetrational

Relateds

tetrate

Synonyms

hyperpower · exponential map · hyper4 · superexponentiation · power tower

Translations (29)

nl tetratie (arithmetic operator consisting of repeated exponentiation) · ja テトレーション (arithmetic operator consisting of repeated exponentiation) · ru тетра́ция (arithmetic operator consisting of repeated exponentiation) · fi tetraatio (arithmetic operator consisting of repeated exponentiation) · uk тетрація (arithmetic operator consisting of repeated exponentiation) · fr tétration (arithmetic operator consisting of repeated exponentiation) · he טטרציה (arithmetic operator consisting of repeated exponentiation) · kk тетрация (arithmetic operator consisting of repeated exponentiation) · sq tetrimi (arithmetic operator consisting of repeated exponentiation) · it tetrazione (arithmetic operator consisting of repeated exponentiation) · pt tetração (arithmetic operator consisting of repeated exponentiation) · pl tetracja (arithmetic operator consisting of repeated exponentiation) · da tetration (arithmetic operator consisting of repeated exponentiation) · cs tetrace (arithmetic operator consisting of repeated exponentiation) · hu tetráció (arithmetic operator consisting of repeated exponentiation) · de Tetration (arithmetic operator consisting of repeated exponentiation) · es tetración (arithmetic operator consisting of repeated exponentiation) · de Potenzturm (arithmetic operator consisting of repeated exponentiation) · ro tetrația (arithmetic operator consisting of repeated exponentiation) · mr टेट्रेशन (arithmetic operator consisting of repeated exponentiation) · gl tetración (arithmetic operator consisting of repeated exponentiation) · kk гипердәреже (arithmetic operator consisting of repeated exponentiation) · id tetrasi (arithmetic operator consisting of repeated exponentiation) · tr tetrasyon (arithmetic operator consisting of repeated exponentiation) · cmn 超-4運算 /超-4运算 (arithmetic operator consisting of repeated exponentiation) · sv tetrering (arithmetic operator consisting of repeated exponentiation) · eo supereksponento (arithmetic operator consisting of repeated exponentiation) · ko 테트레이션 (arithmetic operator consisting of repeated exponentiation) · bg тетрация (arithmetic operator consisting of repeated exponentiation)