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Math Help - Up arrow notation: concept check

  1. #1
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    Up arrow notation: concept check

    Using Knuth's up arrow notation for large numbers:

    m \uparrow\uparrow 6 = m^{m^{m^{m^{m^{m}}}}}

    otherwise referred to as a tower of m's with 6 floors. My question is in regards to the analogy; if I continuously iterate the \uparrow for m \uparrow\uparrow noperator, am I taking that tower and placing a copy of it on every floor of another tower of n floors?

    As in 3 \uparrow\uparrow\uparrow 2 = 3^{27} \Rightarrow  3 \uparrow\uparrow\uparrow\uparrow 2 = (3^{27})^{(3^{27})} ?

    Also would the following simplification work out? 5 \uparrow\uparrow\uparrow\uparrow 3 = 5 \uparrow\uparrow\uparrow 3^{5 \uparrow\uparrow\uparrow 3^{5 \uparrow\uparrow\uparrow 3}}?
    Last edited by Foxlion; May 2nd 2012 at 12:32 AM.
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