A020955

[kohmoto]

    Hi, Seafans.

    I suppose that no one understand what A020955 means.



    So, I explain it a little.

    First of all, see my home page and click “Free Class”, recently I 
rewrote it.



         http://boat.zero.ad.jp/~zbi74583/another02.htm



    The idea “ma”….an abbreviation of “make”….is represented by a 
mapping from subsets of a set to members of the set..

    Because the idea “ma” has the same property as a mapping.



    Number of subsets of a set which has N members is 2^N, and the 
possibility of images of each subsets is N, so number of the mapping 
subsets ->members is N^(2^N).



    But if the set is a model of Free Class then the mapping must satisfy 
some conditions.         .

    They are as follows.



    If the set is {0,1,2,3,….n} then { } ma 0, {0} ma1, {0,1} ma 2, {0,1,2} 
ma 3,….,{0,1,2,3,….n} ma n .



    So, images of n+1 subsets are already decided.

    Hence the number of the mapping or the number of models which has N 
members is N^(2^N-n-1) .



    Yasutoshi


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