🚀 go-pugleaf

In article <1992Oct29.093106.1@tnclus.tele.nokia.fi>,
hporopudas@tnclus.tele.nokia.fi writes:

 One correction to (8):

>
>                   n                       n
>          1     -(x - 1)         1        x - 1   2    1   1/2
>         ---- >  --------- +  ------- ( (--------)  + --- )      (8)
>           n       n   n 2      n   n      n   n       2
>          z      (y - x )     (y - x )    y - x
>

 (8) should be:


                     n                       n
           1     -2(x - 1)         2        x - 1   2    1   1/2
          ---- >  ---------- +  ------- ( (--------)  + --- )      (8)
            n        n   n 2      n   n      n   n       4
           z       (y - x )     (y - x )    y - x


  This has also the form:

            n        n         n   2          n   n 2  (1/2)
           z  < 2 ((x -1) + ((x -1) + (1/4)( y - x )  )     )      (8')


  Could any of you say where the error in the following reasonig ?:
                       -----------------------------------------

  Combining (8') and (7) we have also

              n   2          n   n 2  (1/2)      1     n     n
           ((x -1) + (1/4)( y - x )  )     > ( ------ )  - (x -1)
                                                1/n
                                               2   -1
  From
            n   n          1      2n       n         1    n  (1/2)
           y - x  > 2( ( ------- )   - 2( x - 1) ( ----- )  )
                           1/n                      1/n
                          2   -1                   2   -1

  This also means

           n            1      n
          x  <  (1/2)( ------ )  + 1
             =          1/n
                       2   -1

  This last inequality and the result of prof. Inkeri
  (finnish mathematician), which states that

                3n-4
         x  >  n     ; for n > 3
                             =
  (limitations?)

  We have achieved the following impossible inequality

         3n-4                  1      n    (1/n)
        n     < x <  ((1/2)( ------ )  + 1)
                  =           1/n
                             2   -1

  because left side of the the inequality grows always faster than right
  side of the inequality, when n is greater than 2.



  ---Hannu.