Home Up Prabhakar_for_Fraudigies

 

A  special  entry  from  Mitesh  Jain  &  Mayank  Agarwal ...

GIVEN: Vivek Prabhakar

TO PROVE: nd = nsl + nst   where,

                       nd :     no. of hours in a day

                       nsl :     no. of hours of sleep

                       nst :    no. of hours of studies

PROOF: By Law of Conservation of Time:

          nd = nsl + nst + n0                eqn (1)

          where,

                   n0 :     no. of hours spent in other activities

                             (Like HUGGA, BREAKFAST, LUNCH, DINNER)

                             note: Bathing out of question

          But there exists > 0                s. t.    |n0| <

          where can be made arbitrarily small.

                   ...       n0 à 0

          Using this and eqn (1):

Text Box: nd = nsl + nst
 

 

 

 

                                                         Hence proved.

 

COROLLARY:        nst > nd/2

PROOF: We know that,

                   nst > nsl

          Adding nst both sides:

                   2nst > nsl + nst

          By the above theorem:

Text Box:     2nst > nd
=> nst > nd/2
 

 

                  

 

 

 

 

 

 

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