• Nayuta Ito

    Tale: A long name

    June 24, 2018 by Nayuta Ito

    Note: This tale is not completely original. The original story is entitled "Jugemu," a classical Japanese joke (rakugo). I just made it go wrong with googology.

    Once upon a time, there was an old couple who have just got a son. It's the seventh day of the son, so they have to give him a name. Since they can't come up with a good name, the grandpa went to his friend to get an advice for the name. The friend agreed to give him some idea.

    "OK. Now, what kind of boy do you want him to grow up to?"

    "I just want him to live a long life."

    "A 'long' life?"

    Unfortunately, the friend was a googologist!

    "Now, let's start with a googol. It is one followed by 100 zeroes."

    "Googol Smith. This is a good name. I'll keep it."

    "How about googolplex? It's one follow…

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  • Nayuta Ito

    Here, I'm going to write only what we've agreed on.

    κ is any ordinal, including stage one.

    1. S(1)=Ω
    2. S(κ+1) is the next cardinal after S(κ)
    3. S(κ+T) does NOT the first fixed point of α→S(κ+α).
      1. The n-th fixed point of α→S(κ+α) is denoted by ψ_(S(κ+T))(n),
      2. S(κ+T) is the first fixed point of α→ψ_(S(κ+T))(α).

    Have we already agreed on larger cardinals (Specifically, S(T^2) and larger)? Some people say S(T2)=M_2, instead of I_2. It's a hell!

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  • Nayuta Ito

    I have no idea what I should do.


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  • Nayuta Ito

    This number is from a Japanese googology competition held (technically) a month ago. I am just translating other person's number, so my translation might be wrong. According to the original author, it's bigger than BIG FOOT.


    The alphabets of a formal language FOL is defined as followings:

    in A. Combine P and 16x((P)48(x=t)) by AND operator in FOL and call it Q.

    Whether 80(Q) is provable with A or not depends on m, A, and P. If you take m big enough, 80(Q) is always not provable with A no matter what P is. There exists the mininum of such number m, so take it and add 1. That's the f(n).

    "fight for not being able to write the smallest proof" number is defined as f(10^100).

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  • Nayuta Ito

    See "ill-defined"

    1. The most doubtful and strong system ever.

    1. What computers can't do.

    1. Did you mean: Fish number 1
    2. Did you mean: Fish number 2
    3. Did you mean: Fish number 3
    4. Did you mean: Fish number 4
    5. Did you mean: Fish number 5
    6. Did you mean: Fish number 6
    7. Did you mean: Fish number 7

    1. The smallest googologism.
    2. The biggest googologism.

    1. The biggest number ever.
    2. Just a small number.

    See "badly defined"

    1. What googologists hate the most.
    2. What googologists love the most.

    1. A magic which can get any value of any notation.

    1. Another way of saying ε_0.

    1. Another way of saying zerillion in short scale.
    2. Another way of saying halfillion in long scale.

    1. The only programming language in googology.
    2. The most powerful calculator ever existed.

    1. A number bounded by 10^10^6.

    1. Another way of saying …

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