Definition 2.1. When a and b are integers, we say a divides b if b = ak for some k ∈ Z. We then write a | b (read as “a divides b”). Example 2.2. We have 2 | 6 (because 6 = 2 · 3), 4 | (−12), and 5 | 0. We have ±1 | b for every b ∈ Z. However, 6 does not divide 2 and 0 does not divide 5. Divisibility is a relation, much like inequalities. In particular, the relation 2 | 6 is not the number 3, e...

I magine a society with perfect economic equality. Perhaps out of sheer coincidence, the supply and demand for different types of labor happen to produce an equilibrium in which everyone earns exactly the same income. As a result, no one worries about the gap between the rich and poor, and no one debates to what extent public policy should make income redistribution a priority. Because people e...

That tired Ten-Percent claim pops up all the time. Last year, national magazine ads for U.S. Satellite Broadcasting showed a drawing of a brain. Under it was the caption, "You only use 11 percent of its potential." Well, they're a little closer than the ten-percent figure, but still off by about 89 percent. In July 1998, ABC television ran promotional spots for "The Secret Lives of Men," one of...

An information retrieval performance measure that is interpreted as the percent of perfect performance (PPP) can be used to study the effects of the inclusion of specific document features or feature classes or techniques in an information retrieval system. Using this, one can measure the relative quality of a new ranking algorithm, the result of incorporating specific types of metadata or folk...