On Sun, Apr 29, 2012 at 2:32 AM, Michael Reid <reid@gauss.math.ucf.edu> wrote:
Start with owning the numbers 0 and 1. Each step, with two numbers you already own (perhaps identical), compute A+B, A-B, A*B, A/B, or 2^A. CONJECTURE: the greatest finite real number reachable in N>0 steps is 2^2^2^...^2 with N-1 uses of "^" and evaluating right to left.
OK, in the first step, I compute 1 + 1 = 2 . In the next step, compute 2^2 = 4 (which may as well be 2 + 2 or 2 * 2 ).
But in the third step you want me to do 2^4 , whereas I'd rather do 4^4 , since I already "pwn" 4 . Did I misunderstand something?
A^A is not one of the options.
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