Meaning of tetration | Babel Free

Definitions

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.

uncountable, usually

Equivalents

Examples

“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”

“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.”

“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”

CEFR level