A3notes - Supplementary Course Module A: Simplifying...

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Unformatted text preview: Supplementary Course Module A: Simplifying Numeric Expressions Assignment 3 & Order of Operations; Number Systems Order of Operations: & When evaluating an expression involving more than one arithmetic operation, the evaluation must be carried out following a particular sequence of steps. & The order of precedence when evaluating expressions is described by the acronym BEDMAS: B rackets E xponents D ivision / M ultiplication A ddition / S ubtraction & Nested brackets are simpli&ed by working from inner to outer. & Division / multiplication and addition / subtraction are worked from left to right (recall that division is really just a special form of multiplication, and subtraction is the addition of the negative value). examples: 20 4 2 | {z } +3 = 20 8 + 3 = 15 3 & 5 + 4 2 |{z} = 3 5 + 16 | {z } = 3 (21) = 63 4 + 2 s ( 3) ( 2) + 8 2 3 | {z } 2 = 4 + 2 r ( 3) ( 2) + 8 ( 1) 2 | {z } = 4 + 2 r ( 3) ( 2) | {z } +8 1 = 4 + 2 q 6 + 8 1 | {z } = 4 + 2 p 9 = 4 + 2 (3) = 4 + 6 = 10 Set Notation: & A set is a collection of distinct objects along with a rule to determine if any arbitrary object belongs to the collection or not. & Notation: fg , where indicates the statement (rule) for membership. & statement may be a listing of speci&c objects, an English sentence or a mathematical equation. examples: {house, shoe, tree}, {all WLU students with last name Smith}, f x 2 R j x 2 = 5 g & The objects of a set are called its elements. & if x is an element of set A then we write x 2 A (capital letters usually denote sets, small letters are used for elements) & if a set is denoted by a list, repeated entries are counted only once; thus f 1 ; 2 ; 2 ; 4 ; 4 ; 7 g = f 1 ; 2 ; 4 ; 7 g & A set with no elements is called the empty set, and is written as ? or fg . example: f x 2 R j x 2 = 1 g = ? & Two sets are said to be equal if they have exactly the same members; i.e., sets A and B are equal if x 2 A iff x 2 B . 1 & if A and B are equal sets, we write A = B (or A & B for emphasis, where & means identically equal to, or equivalent) A &nite set has a &nite number of elements; an in&nite set has an in&nite number of elements. Set Operations: Set C is called the intersection of sets A and B if the elements of C are exactly those elements common to A and B ....
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This note was uploaded on 11/25/2010 for the course MATH MA110 taught by Professor Hu during the Spring '10 term at Wilfred Laurier University .

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A3notes - Supplementary Course Module A: Simplifying...

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