Discovery of Real Numbers: Through Traditional Algebra
primes/rationals, irrationals/reals, algebraic properties/order, intervals, absolute value fundamentals, absolute value inequalities/neighborhoods, absolute value theorems, and denseness/completeness
Explore prime and composite numbers and the set of rational numbers.
Explore irrational numbers, the real number system, and the property of denseness.
Covers the algebraic properties of real numbers (commutative, associative, identity, inverse, distributive) and the order properties used to work with inequalities.
Covers open, closed, and half-open intervals, bounded versus unbounded intervals, and their use in describing domains.
Covers the definition of absolute value, its geometric meaning as distance, and solving simple absolute value equations.
Covers solving absolute value inequalities and the concept of a neighborhood or deleted neighborhood of a point.
Covers the multiplicative and quotient properties of absolute value, the Triangle Inequality, and related theorems.
Covers the denseness property, bounded and unbounded sets, and the least upper bound / greatest lower bound (completeness) properties.