Comprehensive coverage of set theory including set notation, set builder notation, element membership, subset relationships, set operations (union, intersection, difference), cardinality, and Venn diagrams. Provides natural numbers, integers notation with extensive examples and exercises.
Comprehensive chapter summary connecting sequences to mathematical induction through recursive reasoning. Reviews arithmetic, geometric, polynomial sequences, characteristic root technique, and induction principles. Includes extensive practice problems covering all sequence types and proof methods.
Introduces strong induction where inductive hypothesis assumes truth for all previous cases, not just immediate predecessor. Uses chocolate bar breaking puzzle and prime factorization to illustrate divide-and-conquer reasoning. Compares to standard induction with ladder metaphor.
Provides extensive practice problems for mathematical induction including summation formulas, divisibility proofs, Fibonacci identities, inequality proofs, geometric formulas, and flawed proof analysis. Covers polygon angles, combinatorics, logarithms, derivatives, and chaining implications.
Explains mathematical induction proof technique for sequences and statements indexed by natural numbers. Covers base case, inductive hypothesis, inductive step structure, and why induction works. Includes examples proving summation formulas and inequality statements with warnings about common errors.