Public learning track
Real Number Systems, Density, and Completeness
12th Grade · Math · Open Global Math
6 lessons
Goal
Analyze decimal and non-decimal representations of real numbers, prove irrationality, and demonstrate the structural density and completeness properties of number systems.
Featured Diagrams
Structural Hierarchy of Number Systems
6 lessons
0 of 6 done
- 1Structural Hierarchy of Number SystemsUp nextStart
- 2Decimal Expansions and Rationality CriteriaPremiumNot started yet
- 3Non-Decimal Base Representations of Real NumbersNot started yet
- 4Rigorous Proofs of IrrationalityNot started yet
- 5Density of Rational and Irrational NumbersNot started yet
- 6Incompleteness of the Rationals and the Supremum PropertyNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
6 lessons
Real Number Systems, Density, and Completeness
Analyze decimal and non-decimal representations of real numbers, prove irrationality, and demonstrate the structural density and completeness properties of number systems.
2
5 lessons
Advanced Radicals, Polynomial Division, and Algebraic Fractions
Manipulate algebraic expressions with rational exponents and surds, apply polynomial division and theorems, and simplify complex algebraic fractions.
3
5 lessons
Partial Fraction Decomposition Techniques
Decompose proper and improper rational functions into partial fractions with linear and repeated linear denominator factors.
4
6 lessons
The General Binomial Theorem and Power Approximations
Expand binomial expressions for positive integers and generalize to rational exponents with convergence criteria to approximate numerical and functional values.
5
7 lessons
Sequences, Recurrence Relations, and Series Convergence
Analyze explicit and recursive sequences, evaluate finite and infinite series in sigma notation, determine convergence, and model real-world dynamic phenomena.