Repetitive addition is called multiplication.
Repetitive multiplication is called exponentiation.
Repetitive exponentiation must be the 4th operation if addition is the 1st operation.
x^(x^(y-1)=z works. ie 3 (4th op) 4 = 7.6 *10^12, 3 (4th op) 3 = 19683.
Is there a math book that includes this as a valid fundamental operation?
Repetitive multiplication is called exponentiation.
Repetitive exponentiation must be the 4th operation if addition is the 1st operation.
x^(x^(y-1)=z works. ie 3 (4th op) 4 = 7.6 *10^12, 3 (4th op) 3 = 19683.
Is there a math book that includes this as a valid fundamental operation?
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Iterated exponentiation is called tetration. The Wikipedia page I've linked below gives a good overview of the operation. I'm not familiar with any textbooks which introduce tetration as part of a usual curriculum -- while it's quite interesting in its own right, I don't believe it has a great deal of applications or connections to other areas of mathematics.
I believe you've applied it mistakenly though -- 3 ^^ 3 should be computed as "three to its own power three times," or 3^3^3 = 3^(27) = 7,625,597,484,987.
I believe you've applied it mistakenly though -- 3 ^^ 3 should be computed as "three to its own power three times," or 3^3^3 = 3^(27) = 7,625,597,484,987.
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That's understandable, but the reason it's defined to go right to left is because otherwise it just reduces to exponentiation to a product power. (3^3)^3 is the same as 3^(3*3) = 3^9. Tetration grows much more quickly than exponentiation.
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