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December 1st, 2013, 07:54 PM   #1
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Alternate form for floor function

Is there another way to express



that doesn't involve as much ceiling functions?
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December 5th, 2013, 12:00 PM   #2
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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 = (Y-r)/X

So you found k, that's in turn the floor of Y/X
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December 5th, 2013, 12:07 PM   #3
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Re: Alternate form for floor function

Quote:
Originally Posted by AlephUser
So you found k, that's in turn the floor of Y/X
Yes, and that's of no theoretical, let alone computational use.
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