Monday, October 13, 2014

nth operation

n-th operation.  The successor function outputs a natural number that is one greater than the input (n=1).  Addition is repeated use of the successor function (n=2).  Multiplication is repeated addition (n=3).  Exponentiation is repeated multiplication (n=4).  Towers of powers are repeated exponentiation (n=5).  ??? are repeated towers of powers (n=6)?  ??? are repeated ??? (n=7)?

The number of atoms in the universe is estimated to be 10^80 atoms.  The required computation would involve just the level of exponentiation.  So it boggles the mind how the numbers involved get so big so fast.

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