The division of 0 by 0 results in a NaN. A nonzero number divided by 0, however, returns infinity: 1/0 = , -1/0 = -. The reason for the distinction is this: if f(x) 0 and g(x) 0 as x approaches some limit, then f(x)/g(x) could have any value. For example, when f(x) = sin x and g(x) = x, then f(x)/g(x) 1 as x 0. But when f(x) = 1 - cos x, f(x)/g(x) 0. When thinking of 0/0 as the limiting situation of a quotient of two very small numbers, 0/0 could represent anything. Thus in the IEEE standard, 0/0 results in a NaN. But when c > 0, f(x) c, and g(x)0, then f(x)/g(x) ±, for any analytic functions f and g. If g(x) < 0 for small x, then f(x)/g(x) -, otherwise the limit is +. So the IEEE standard defines c/0 = ±, as long as c 0. The sign of depends on the signs of c and 0 in the usual way, so that -10/0 = -, and -10/-0 = +.