Slidecast supplement to Blitzer's Thinking Mathematicall, 4th edition, Section 13.1 Mathematical Systems

1. Supplement toSection 13.1, Mathematical Systems(Blitzer, Thinking Mathematically, 4e) By Gideon Weinstein

2. Mathematical Systems A set of elements AND at least one binary operator. “Things” AND rules for “actions combining two.” Examples: Integers AND addition Real numbers AND multiplication and addition Turns of a three-way switch AND combining turns consecutively

3. Properties of Some Systems GOAL: Given a system, you should be able to identify which properties it has. Closure “can’t get out” Commutative “swap here for there” Associative “either one is the same” Identity “something makes no change” Inverse “the opposite exists”

4. Symbols & Notation Usually +, -, x, ÷ are reserved for the usual operations on the usual number systems Sometimes, * or •replaces x Sometimes, the + symbol is used for unusual systems where the operation is very similar to ‘regular addition’ (like addition of vectors) Usually, a “weird” symbol like #, %, & is used to indicate that the operation is VERY UNLIKE the regular operations