Very big numbers

Discussion in 'Recreational Math' started by Ravi Kulkarni, Dec 18, 2003.

  1. Everyone knows about numbers like googol (10^100) and googolplex (10^googol).
    For fun my son and I came up with the following nomenclature:

    10^googolplex = 1 googolduplex
    10^googolduplex = 1 googoltriplex
    10^googoltriplex = 1 googolquadruplex

    and fun numbers like

    1 googolcentplex (above procedure repeated 100 times)
    1 googolmilleplex (repeated 1000 times)
    1 googolmegaplex (repeated million times)
    1 googolgigaplex (repeated billion times)
    1 googolteraplex (repeated trillion times)
    1 googolpetaplex (repeated quadrillion times)

    and so on.

    Ravi Kulkarni
     
    Ravi Kulkarni, Dec 18, 2003
    #1
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  2. | Everyone knows about numbers like googol (10^100) and googolplex (10^googol).
    | For fun my son and I came up with the following nomenclature:
    |
    | 10^googolplex = 1 googolduplex
    | 10^googolduplex = 1 googoltriplex
    | 10^googoltriplex = 1 googolquadruplex
    |
    | and fun numbers like
    |
    | 1 googolcentplex (above procedure repeated 100 times)
    | 1 googolmilleplex (repeated 1000 times)
    | 1 googolmegaplex (repeated million times)
    | 1 googolgigaplex (repeated billion times)
    | 1 googolteraplex (repeated trillion times)
    | 1 googolpetaplex (repeated quadrillion times)
    |
    | and so on.
    |
    Actually, if you ask a set theorists, these numbers aren't big at all, since
    they are still "reachable" (even better: they are natural numbers)...
    But I'm afraid I can't give a good definition of which njumbers are reachable
    and which aren't.

    Math rules!
    H.
     
    Hendrik Maryns, Dec 19, 2003
    #2
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  3. He's a bit slow.
    google = 10^100
    googleplex = googgle^googgle
    googleduplex = googleplex^googleplex
    ....

    But a whiz kid even faster
    google = 10^100
    googleplex = google^(google^(google^...)), google number of times
    googleduplex = googleplex^googleplex^...^googleplex,
    googleplex number of times
    ....

    Are you up to speed now?
    Oh, one more thing. Google is so small, so jump the gun with
    google = 10^trillion. Naw, still not big enuf, let
    google = 10^(US national debt)

    To join the jet set go google on
    'Graham's number' and 'Kunth's arrow notation'.
    Look also for notion ^, ^^, ^^^, ...
    a^b = a^b
    a^^b = a^b^b^b...^b, b times
    a^^^b = a^^b^^b^^b...^^b, b times
    ....
    and Ackermann function, giants amonst the hypergoogleplexed ants.

    All the above read with convention of right association, ie
    a^b^c = a^(b^c) as a^b^c = (a^b)^c = a^bc so mundane.

    Riddle of the day:
    can the mushrooming national debt be hidden under the Bush?
     
    William Elliot, Dec 19, 2003
    #3
  4. Ravi Kulkarni

    Peter Webb Guest

    <SNIP>

    Untrue. The Googolplex (like the google) was defined by the 10 year old son
    of one of the authors of the classic Courant & Robbins: What is
    Mathematics?. He defined a "1 with a googol of zeroes" which is of course
    10^googol.
     
    Peter Webb, Dec 19, 2003
    #4
  5. Ravi Kulkarni

    Phil Carmody Guest

    Edward Kasner named the googolplex, his nephew named the google, as I remember it.

    Phil

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    Phil Carmody, Dec 19, 2003
    #5
  6. Blah, you miss my point which is to consider the series,
    instead of the pickayunne names you call it.
     
    William Elliot, Dec 20, 2003
    #6
  7. Ravi Kulkarni

    Peter Webb Guest


    You may be right. I pulled out my copy of What is Mathematics - sighed
    deeply when I saw that I purchased it in 1972 and probably haven't opened it
    in 30 years - and google doesn't appear in the index.
     
    Peter Webb, Dec 20, 2003
    #7
  8. Ravi Kulkarni

    Phil Carmody Guest

    /Mathematics and the Imagination/ by Kasner and Newman
    ( http://www.amazon.com/exec/obidos/A...5942065/sr=1-1/ref=sc_b_1/104-4126383-2740715 )
    was the second book I ever bought. I believe that had a tiny anecdote about
    the naming. However, I no longer have teh book with me. Before posting my
    last post I made sure I went via
    mathforum.org/library/drmath/view/57575.html
    to check that I wasn't misremembering.
    Try a search engine for that term :)


    Phil
     
    Phil Carmody, Dec 20, 2003
    #8
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