tetration
Language: English
Part of speech: noun
Pronunciation: ipa: /tɛˈtɹeɪʃn̩/
ipa: /tɛˈtɹeɪʃən/
rhymes: -eɪʃən
Forms: form: tetrations
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).
Senses: examples: text: 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
ref: 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:
text: 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.
ref: 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:
text: 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
ref: 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:
topics: arithmetic
synonyms: exponential map
hyper4
hyperpower
power tower
superexponentiation
glosses: 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.
Coordinate terms: word: addition
word: exponentiation
word: hexation
word: multiplication
word: pentation
word: succession
word: successor
sense: addition, summation
english: addend; total
translation: addend; total
alt: augend
word: + =
sense: addition, summation
english: sum
translation: sum
alt: summand
word: + +... =
sense: subtraction
roman: subtrahend
english: difference
translation: difference
word: − =
sense: multiplication, factorization; multiplier
roman: multiplicand
english: product
translation: product
word: × =
sense: multiplication, factorization; factor
english: factor; factor; product
translation: factor; factor; product
word: × ×... =
sense: division; dividend
roman: quotient
word: ÷ =
sense: numerator) / (denominator) = (quotient
english: with remaining
translation: with remaining
alt: quotient
word: Or sometimes
sense: exponentiation; base
english: power
translation: power
alt: exponent
word: =
sense: root extraction; degree
roman: radicand
word: √ =
sense: logarithmization
english: logarithm
translation: logarithm
alt: antilogarithm
word: log(base) =
Derived terms: tetrational
Related terms: tetrate