Tetration is a binary mathematical operator defined by the recurrence relation: More intuitively, with b copies of a. is pronounced "a tetrated to b" or "to-the-b a." Tetration leads to very large numbers, even with small inputs. For example, , which has 3638334640025 digits.
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| - Tetration is a binary mathematical operator defined by the recurrence relation: More intuitively, with b copies of a. is pronounced "a tetrated to b" or "to-the-b a." Tetration leads to very large numbers, even with small inputs. For example, , which has 3638334640025 digits.
- Tetration, also known as hyper4, superpower, superexponentiation, superdegree, powerlog, or power tower, is a binary mathematical operator defined as \(^yx = x^{x^{x^{.^{.^.}}}}\) with \(y\) copies of \(x\). In other words, tetration is repeated exponentiation. Formally, this is \[^0x=1\] \[^{n + 1}x = x^{^nx}\] where \(n\) is a nonnegative integer. Tetration is the fourth hyper operator, and the first hyper operator not appearing in mainstream mathematics. When repeated, it is called pentation. If \(c\) is a non-trivial constant, the function \(a(n) = {}^nc\) grows at a similar rate to \(f_3(n)\) in FGH.
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| - Tetration is a binary mathematical operator defined by the recurrence relation: More intuitively, with b copies of a. is pronounced "a tetrated to b" or "to-the-b a." Tetration leads to very large numbers, even with small inputs. For example, , which has 3638334640025 digits.
- Tetration, also known as hyper4, superpower, superexponentiation, superdegree, powerlog, or power tower, is a binary mathematical operator defined as \(^yx = x^{x^{x^{.^{.^.}}}}\) with \(y\) copies of \(x\). In other words, tetration is repeated exponentiation. Formally, this is \[^0x=1\] \[^{n + 1}x = x^{^nx}\] where \(n\) is a nonnegative integer. Tetration is the fourth hyper operator, and the first hyper operator not appearing in mainstream mathematics. When repeated, it is called pentation. If \(c\) is a non-trivial constant, the function \(a(n) = {}^nc\) grows at a similar rate to \(f_3(n)\) in FGH. Daniel Geisler has created a website, tetration.org, dedicated to the operator and its properties.
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