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Summary of Material
1. Numbers, Sets, and Sequences
Rational Zeros Theorem. For polynomials of the form cnxn + … + c0 = 0 , where each coefficient is an integer, then the only rational solutions have the form $\frac{c}{d}$ where c divides cn and d divides c0; rational root r must divide c0.
The maximum of a set S is the largest element in the set. The minimum is the smallest element in the set. The $\inf$ of S is the greatest lower bound. The $\sup$ of S is the smallest upper bound. S is bounded if $\forall$s $\in$ S, s$\leq$M for some M $\in$ $\reals$ Completeness Axiom. If S is a nonempty bounded set in $\reals$, then $\inf$ S and $\sup$ S exist. Archimedean Property. If a, b $\gt$ 0, then $\exists$n such that na $\gt$ b.
