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December 1st, 2013, 08:54 PM  #1 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Alternate form for floor function
Is there another way to express that doesn't involve as much ceiling functions? 
December 5th, 2013, 01:00 PM  #2 
Member Joined: Aug 2012 Posts: 40 Thanks: 3  Re: Alternate form for floor function
Let X and Y be positive integers. I'll assume X<Y and that Y isn't divisible by X. Then rewrite Y as: Y = kX+r, where k and r are integers, and 0 < r < X < Y So, if you divide the equation by X: Y/X = k+r/X Well, you can see that K is an integer and that r/X is the decimal part of Y/X We could then rewrite the first equation as: Y  r = kX And as such: k = (Yr)/X So you found k, that's in turn the floor of Y/X 
December 5th, 2013, 01:07 PM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Alternate form for floor function Quote:
 

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