> 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". It probably 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)
 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".