tetration

English

Etymology

tetra- +‎ (itera)tion; coined by Reuben Goodstein

Pronunciation

• IPA^(key): /tɛtˈɹeɪʃən/
• Rhymes: -eɪʃən

Noun

tetration (usually uncountable, plural tetrations)

1. (arithmetic) 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. Notation: ^ba, a↑↑b or a→b→2

Synonyms

• exponential map, hyper4, hyperpower, power tower, superexponentiation

Coordinate terms

• succession
• addition
• multiplication
• exponentiation
• pentation
• hexation

Other terms used in arithmetic operations:

• successor
• addition, summation:

  (augend) + (addend) = (total)

  (summand) + (summand) + (summand)... = (sum)

• subtraction:

  (minuend) − (subtrahend) = (difference)

• multiplication, factorization:

  (multiplier) × (multiplicand) = (product)

  (factor) × (factor) × (factor)... = (product)

• division:

  (dividend) ÷ (divisor) = (quotient)

  (numerator) / (denominator) = (quotient)

  Or sometimes = (quotient) with (remainder) remaining

• exponentiation:

  (base) ^(exponent) = (power)

• root extraction:

  ^(degree) √ (radicand) = (root)

• logarithmization:

  log_(base) (antilogarithm) = (logarithm)

Advanced hyperoperations: tetration, pentation, hexation

Translations

Translations

• Chinese:

  Mandarin: 超-4運算／超-4运算

• Finnish: tetraatio (fi)
• German: Tetration f
• Italian: tetrazione f
• Polish: tetracja f