Comments by "EebstertheGreat" (@EebstertheGreat) on "The Four 4s - Numberphile" video.

  1. I like this solution for a minimal set of operations {-, log, √}. Here, - is binary (subtraction, not negation), as is log, but √ is the unary principle square root function. Only real arithmetic is required. ... -(4+n) = [log_(√4) log₄ √√√...√√√4] - 4 with n √'s before the penultimate 4 ... -4 = [log_(√4) log₄ 4] - 4 -3 = log₄ 4 - log_(√√4) 4 -2 = 4 - 4 - (4 - √4) -1 = 4 - 4 - log₄ 4 0 = 4 - 4 - (4 - 4) 1 = log₄ 4 - (4 - 4) 2 = 4 - √4 - (4 - 4) 3 = [log_(√√4) 4] - log₄ 4 4 = 4 - log_(√4) log₄ 4 ... 4+n = 4 - log_(√4) log₄ √√√...√√√4 with n √'s before the final 4 ...
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  2. [4/4]% = 1% = 0.01, not 100.
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