Michael Somos on Sun, 31 Oct 1999 08:42:21 -0500 (EST)

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Re: Euclidean division

Bill Allombert wrote :

> I do not know what is the euclidean quotient of two rational.
> Perhaps (a/b)\(c/d)=ad\bc ?

I think the natural definition is :  x\y = floor(x/y)  which makes
sense even for real x and y. Note that this is a natural step in
the Euclidean algorithm. In order for one quantity to "measure"
another you have to subtract the smaller from the larger a number
of times. The number of times required is the Euclidean quotient.
Shalom, Michael

Michael Somos <somos@grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115