```Date: Nov 20, 2013 4:27 AM
Author: Jussi Piitulainen
Subject: Re: Help with formula (revised question)

William Elliot writes:> On Wed, 20 Nov 2013, Robert Crandal wrote:> > > Here is the new data set:> > > > X         Y> > --         --> > 0.0       1> > 0.1       1> > 0.5       1> > 0.9       1> > 1.0       1> > 1.03     2> > 1.5       2> > 1.8       2> > 2.0       2> > 2.3       3> > 3.0       3> > 3.2       4> > > > Can this data be represented with a formula> > that only uses either addition, subtraction,> > multiplication, division, modulus, or the power (^)> > function, or any combination of these?>  > No, the function is ceiling x = -floor -x.  It's a well accepted> function even availible in some computer languages.  Before> computers, mathematicians used [x] for the greatest interger <= x,> which computer languages call floor or int(), as in basic.Define "x mod y" for arbitrary reals, y not 0, by   x mod y = x - y * floor(x/y)and pretend this is what the question referred to as "modulus"[1]. Itprobably isn't, but for a moment, pretend.Then x mod 1 is the fractional part, floor(x) = x - (x mod 1) and:   ceiling(x) = -floor(-x)              = -((-x) - ((-x) mod 1)) = x + ((-x) mod 1)[1] The book I'm following calls floor(x/y) the quotient and (x mod y)the remainder; the modulus is y, aka "the number after mod".
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