wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> Floor function quotient
        
(Message started by: NickH on Mar 15^th, 2003, 10:29am)

Title: Floor function quotient
Post by NickH on Mar 15^th, 2003, 10:29am

Let x be a real number and n a positive integer. Show that

[nx]/n] = [x],

where [x] is the greatest integer less than or equal to x.

Title: Re: Floor function quotient
Post by towr on Mar 16^th, 2003, 7:56am

...[hide]
[n x ]/n]
=
[n * ([x]+ x-[x]) ]/n]
=
[n * [x] + n * (x-[x]) ]/n]
= {n * [x] is integer}
[x] + [n * (x-[x]) ]/n]
= {n * (x-[x]) < n}
[x]
= [x]
[/hide]...