Tamara Fisher -- In mathematics, the term "equal" is used when things are "equal in value," and being equal in value is what was intended with those daring strokes of 1776. It meant that the man sweeping the floor and the merchant running the business were of equal value - equal in the eyes of the law, equal in their value as humans, equal in their right and opportunity to pursue their happiness.
Deborah Meier -- Yes, E.D. Hirsch is right: You can't measure reading qua reading. I not merely observed but ran little mini-focus groups to understand why some kids got "right" answers and others "wrong" ones. It had little to do with their reading skill.
Michael J. Petrilli -- We need to stop having these extreme arguments, between “No excuses!” on one side and “It’s all about poverty!” on the other. Poverty matters immensely. Schools matter immensely. Let’s get on with addressing both.
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic. Every transcendental number is irrational.
A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.