tetration

tetration englanniksi

1. The 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 \ldots to the power of a, in which a appears b times.

(synonyms)

3. (quote-book)|year=1993|page=39|pageurl=https://books.google.com/books?id=X429EAr8g4kC&pg=PA39|isbn=978-0-671-74282-9|passage=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.

4. (quote-book)|year=2016|page=11|pageurl=https://books.google.com/books?id=KC0WDAAAQBAJ&pg=PA11|doi=10.1007/978-1-4842-1892-1|isbn=978-1-4842-1891-4|passage=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^{2^{2^2. (..) Needless to say, on positive whole numbers, tetration causes values to grow incredibly fast. This probably helps explain why it's not too practical in real life: after all, the simple operation of exponentiation allows us to concisely express the number of atoms in the universe, approximately 10^{80}, or a 1 with 80 zeros. (..) But even without real-life applications, there are some mathematicians that find tetration a very interesting topic to study. On small numbers, it can have some bizarre properties. For example, get out a calculator and try calculating some tetrations of the square root of 2.