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?, exponentiation, multiplication, addition, ?

  1. May 10, 2007 #1
    What simple operations, if any, precede or succeed the series ". . . exponentiation, multiplication, addition. . ."?
  2. jcsd
  3. May 10, 2007 #2
    ..., hexation, pentation, tetration, exponentiation, multiplication, addition, ...

    Maybe succession is a good candidate for the next operation in the sequence. I don't think there's much after that, though.
  4. May 11, 2007 #3


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    Are you trying to remember PEMDAS?

    - Warren
  5. May 11, 2007 #4

    More like: multiplication represents repeated additions, and exponentiation represents repeated multiplications, etc. (Thanks for the PEMDAS blast to my algebraic past, though.)
  6. May 11, 2007 #5
    Yep, that's the list I gave you.

    Tetration ([itex]\uparrow\uparrow[/itex]) is repeated exponentiation, right associated:

    [tex]a\uparrow\uparrow b = a^{a^{...^{a^a}}}[/tex]

    where there are [itex]b[/itex] [itex]a[/itex]'s on the left side.

    [tex]2\uparrow\uparrow 2 = 2^2 = 4[/tex]
    [tex]2\uparrow\uparrow 3 = 2^{2^2} = 2^4 = 16[/tex]
    [tex]2\uparrow\uparrow 4 = 2^{2^{2^2}} = 2^{16} = 65536[/tex]

    Pentation ([itex]\uparrow\uparrow\uparrow[/itex]) is repeated tetration, also right associated, etc.

    Succession is adding 1, so you might say that adding a and b is like adding 1 to a, b times.

    EDIT: I use Knuth uparrow notation for the higher operators. This is not strictly speaking a universally agreed upon thing, so you might have to explain it to pretty much anyone you show it to.
    Last edited: May 11, 2007
  7. May 11, 2007 #6

    That's what I sought. "Succession" as you define it seems reasonable to me. My guess is that the next step involves fractals.
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