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A3notes - Supplementary Course Module A Simplifying Numeric...

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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 2 | {z } +3 = 20 ± 8 + 3 = 15 3 ° 5 + 4 2 |{z} ± = 3 ² 5 + 16 | {z } ³ = 3 (21) = 63 4 + 2 s ( ± 3) ( ± 2) + 8 ± ² 2 ± 3 | {z } ³ 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: f³ ³ ³ g , where ³ ³ ³ 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 f g . 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
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° 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 . ° C = A \ B = f x j x 2 A and x 2 B g example: f 1 ; 2 ; 5 ; 9 ; 7 g \ f± 3 ; 4 ; 5 ; 7 g = f 5 ; 7 g ° Set D is the union of sets A and B if D consists of those elements which are either in A or in B or in both.
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