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  • Deedlit11

    My humble extension of FOOT

    December 22, 2016 by Deedlit11

    Welp, other people have gotten into trying to beat FOOT, so I figured I might as well try my hand at it.

    With a decided lack of originality, I've decided to name my system FOFT (First Order Functional Theory). As the name suggests, the fundamental new objects are functionals on ordinals. Functionals are defined as follows:

    Let \(F_\alpha\) denote the set of \(\alpha\)-functionals.

    A 0-functional is just an ordinal.

    A \(n+1\)-functional is a function from \(F_n\) to \(F_n\). Equivalently, it is a function from \(\prod_{i=1}^n F_i\) to \(F_0\). (You can see this by repeatedly applying the definition of \(F_i\) in the range - for example, \(f: F_3 \mapsto F_3 \implies f: F_3 \mapsto (F_2 \mapsto F_2) \implies f: F_3 \mapsto (F_2 \mapsto (F_1 \map…

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  • Deedlit11

    Okay, the Second Googological Olympiad has officially ended.  Four people sent in solutions, and two sent in solutions to all six problems.  The winner is Wojowu, who scored a stellar 47 out of 50 points. On April 15, a person named January First-of-May sent in solutions; while technically his scores should not count, I don't see a problem with adding his scores to the list.


    Results of the Second OlympiadNameP 1P 2P 3P 4P 5BonusTotalWojowu55101010747Wythagoras55596131Cloudy17655    10January First-of-May55    10cookiefonster5     5


    Thanks to everyone who participated! I had a lot of fun writing and overseeing the contest.


    Solution to Problem #1:

    The answer is \(\prod_{i=0}^{n-1} 10[3]i\), where we take \(10[3]0\) to be \(10\). In fact \(10[3]n…




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  • Deedlit11

    Welcome to the Second International Googological Olympiad! Rules are as follows:

    • There are 5 questions and a bonus question, worth a total of 50 points.
    • Contest ends at 23:59 PST on April 12, 2015.
    • Solutions are to be mailed to my e-mail address. It is an account at hotmail.com, and the user name is my name (Royce Peng).
    • If anyone needs clarification, please bring it up in the comments. However, please do not spoil any question by giving away the answer or saying something that gives insight into solving the problem. If you cannot do so, or are not sure whether your comment will be a spoiler for the problem, please e-mail me with your question instead.
    • Please do not discuss the problems with each other before the due date.
    • I will try to respond …
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  • Deedlit11

    So, I'm thinking of starting the next Googological Olympiad shortly, and I was wondering whether people had any comments regarding how it should be administered.

    How long should I run it for?

    Should I give immediate feedback, or wait until the competition is over?

    If I give feedback, should I allow resubmission of solutions?

    I was thinking of varying the number of points each question is worth. Is this a good or bad idea?

    Thanks in advance for any comments!

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  • Deedlit11

    Bignum Bakeoff appetizer

    September 15, 2014 by Deedlit11

    Vell mentioned the idea of starting a new Bignum Bakeoff.  I hope that happens, but here is a closely related problem that could serve as an appetizer to the big contest.

    Namely, write a program using the shortest number of characters that implements a function with growth rate comparable to \(f_{\varepsilon_0} (n)\). My first interest is using the language C, but you can program in any language you want - each language will be a different category of course.

    Some rules:

    1. The program must return a number at least \(f_{\omega^{\omega^{\omega^\omega}}}(4)\).  (Nothing really special about this number, just wanted to pick a number big enough to require an epsilon_0 function but not much bigger.)

    2. It is assumed that every language has integer …

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