MATB24H3 Study Guide - Final Guide: Scalar Multiplication, Additive Inverse, Multiplication Table
Document Summary
A set is simply a collection of objects. We will use among other sets the following: Z : the set of integers (positive, negative, or zero). Q : the set of all rational numbers= { p q (cid:12) (cid:12) (cid:12) (cid:12) p, q z, q 6= 0} Zn : the set of integers from 0 to n 1 inclusive. Note: it is important not to assume anything about newly de ned sets with addition and multiplication. It is never assumed that the identities ex- ist. They must be found and they may not be what seem to be the obvious choices from the elements of the given set. Here are some examples of elds: the set of the real numbers with the usual addition and multiplication. Verify this result as an exercise: the set of all rational numbers with the usual addition and scalar multiplication, the set z3 with the addition and multiplication given in the following tables:
