Array notation

Array notation is a kind of notation for large numbers. Comparing to combinatoric functions, array notation has more complex definition, but easier to evaluate. We’ve known some array notations, such as Bowers’ exploding array function (BEAF), Bird’s array notation (BAN), extensible-E system (ExE), and hyperfactorial array notation (HAN).

Here I bring a strong array notation, and it goes far away from the notations mentioned above. It’s made up of several parts shown below.

These 5 parts don’t work.

After fixing the problem in NDAN, we have these parts.


43 thoughts on “Array notation

  1. Samuel Fields says:

    I would like to ask a few questions about functions and algorithms. So addition is the function and add or adding is the algorithm, multiplication is the function and multiply or multiplying is the algorithm, exponation is the function and exponate or exponating is the algorithm, tetration is the function and tetrate or tetrating is the algorithm. Is this correct?


  2. Samuel Fields says:

    Does anyone know how many symbols it would take to define (pDDN) in the language of First Order Set Theory (FOST)?


  3. Aarex Tiaokhiao says:

    SAN can be extended: +’ is dropper-droppers for ::::…+ and ++ is dropper-droppers for +::::…, then we can defined nested droppers for +++…., like (N^+)


    • The value of TREE(3) is too hard to work out. It has a lower bound of s(3, s(3, 262138 {1 {1`1,2 `} 2} 2) {1 {1`1,2 `} 2} 2 {1 {1`1,2 `} 5} 2). However, its upper bounds are much weaker, because we don’t know the growth rate of TREE(n). We just know TREE(3)<SSCG(3), where SSCG(n) grows slower than s(n,n{1,,2,2}2).
      So s(3, s(3, 262138 {1 {1`1,2 `} 2} 2) {1 {1`1,2 `} 2} 2 {1 {1`1,2 `} 5} 2) < TREE(3) << s(3,3 {1,,2,2} 2).


  4. Samuel Fields says:

    Hypcos how would you describe a Golapulus (10^100 & 10 & 10) with your Strong Array Notation?
    Where would a Golapulus be in your Strong Array Notation?


  5. Samuel Fields says:

    Hypcos how would you describe a 10^100 array of 10s array of 10s with your Strong Array Notation?


    • Samuel Fields says:

      Aarex I am a huge fan of your work with large numbers. I have been studying your work with large numbers for years. Could you show me the steps to go from Otoperoogol to Otopersuperoogol? These numbers are listed on your Extensible Up-arrow System part 4 Dimensional/Nested Array Up-arrow webpage.


        • Username5243 says:

          The question was asked before you closed it, silly. And I’m sure he’ll find the time to bring back the extended arrow notation some time in the future…

          And he’s made primary dropper-dropping notation, part 12. Whether he plans to make a part 13, I don’t know.


    • Deedlit says:

      It seems like he already has. (or at least tried to) The new NDAN is a replacement for the old one, and WDEN and mWDEN are analogues to DEN and mDEN. WDmEN seems to go a different direction from soDEN and hoDEN; perhaps he sees this as a better/stronger way to extend things.



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