Measure of apporoximation

[kohmoto]

    >"RE : Almost Integer"
    Members who responded me.
    Thanks for your good explanations.
    I understood well.

    >Ed Pegg Jr
    I read your column on MAA site.
    It is nice!!

    I think that my "nega entropy" for an algorithm is equivalent as your 
"keenness" for an approximation.

         Definition of E(a) :
         If a=algorithm then,

         E(a)=1-log{search area of a}/log{object of a}

         Comment : If you want, put "-" for "nega"

         Example1: Prime test
         Divide N by k , k=0 to N^(1/2)

         E(P)=1-log(N^(1/2)/logN=1-1/2=0.5

         Example2 : Unitary Amicable pair's record.
         It has 317 digits.
         I searched 10^8 candidates.

         E(UA)=1-8/317=0.975

　　　　　　
    The relationship between E and K.
         If K(a)=keenness of an approximation then,

         E(a)=1-1/K(a)=1-{digits used}/{digits of accuracy}

         Example1 :
         If digits of accuracy is infinity, then it has exact information.
         Indeed, E(a)=1-n/infinity=1

         Example2 :
         If digits of accuracy is the same as digits used, then it has no 
information.
         The entropy is calculated as follows. E(a)=1-1/1=0 .

    Yasutoshi