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tegrates
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There are 8 letters in TEGRATES ( A1E1G2R1S1T1 )
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In mathematics, Tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation. The word was coined by Reuben Louis Goodstein, from tetra- (four) and iteration. Tetration is used for the notation of very large numbers. The notation * * * * * * * * n * * * a * * * * {\displaystyle {^{n}a}} * means * * * * * * a * * * a * * * ⋅ * * * ⋅ * * a * * * * * * * * * * * * {\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}} * , the application of exponentiation * * * * n * − * 1 * * * {\displaystyle n-1} * times. * Shown here are the first four hyperoperations, with tetration as the fourth (and succession, the unary operation denoted * * * * * a * ′ * * = * a * + * 1 * * * {\displaystyle a'=a+1} * taking * * * * a * * * {\displaystyle a} * and yielding the number after * * * * a * * * {\displaystyle a} * , as the 0th):* Addition * * * * * a * + * n * = * a * + * * * * * 1 * + * 1 * + * ⋯ * + * 1 * * ⏟ * * * * n * * * * * {\displaystyle a+n=a+\underbrace {1+1+\cdots +1} _{n}} * * n copies of 1 added to a. * Multiplication * * * * * a * × * n * = * * * * * a * + * a * + * ⋯ * + * a * * ⏟ * * * * n * * * * * {\displaystyle a\times n=\underbrace {a+a+\cdots +a} _{n}} * * n copies of a combined by addition. * Exponentiation * * * * * * a * * n * * * = * * * * * a * × * a * × * ⋯ * × * a * * ⏟ * * * * n * * * * * {\displaystyle a^{n}=\underbrace {a\times a\times \cdots \times a} _{n}} * * n copies of a combined by multiplication. * Tetration * * * ... |