What is a tetration? (Repeated exponentiation)
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The number ⁴2 is a type of number called a "tetration" which may also be expressed using Knuth's up-arrow notation 2↑↑4.
Tetration is a mathematical operation that represents repeated exponentiation. It is an extension of exponentiation, which itself is an extension of multiplication. In tetration, the base number is raised to the power of itself multiple times in a nested fashion.
The notation for tetration is often expressed as ⁿa, where a is the base and n is the height or the number of iterations. For example:
ⁿa = a^a^a^...^a, n times
Here, a is repeated n times as the exponent.
To illustrate, let's take ³2 as an example:
³2 = 2^2^2
This is equivalent to 2^4, which is 16.
Tetration grows very rapidly, and for larger values of n, the result becomes extremely large. It is a concept used in advanced mathematics and is not as commonly encountered as addition, multiplication, or even exponentiation in everyday mathematics.
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