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Math 105 Notes- Week 1

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by: Cassandra Notetaker

Math 105 Notes- Week 1 MATH 105

Cassandra Notetaker
Edinboro University of Pennsylvania
GPA 4.0
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About this Document

These notes cover Review Section 1 in the College Algebra textbook
College Algebra
Dr. Phillip Funtulis
Class Notes
Math, Algebra




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This 3 page Class Notes was uploaded by Cassandra Notetaker on Saturday January 23, 2016. The Class Notes belongs to MATH 105 at Edinboro University of Pennsylvania taught by Dr. Phillip Funtulis in Spring 2016. Since its upload, it has received 44 views. For similar materials see College Algebra in Mathematics (M) at Edinboro University of Pennsylvania.

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Date Created: 01/23/16
Funtulis- MATH 105 Review Section 1: Sets - 1/20/16 Set- a collection of any objects of our intuition; a well-defined collection of any objects (physical or abstract). Well-Defined- the set is not biased; one is able to determine what is in the set. Ex. {all great actresses} since “great” is a relative term, this set would be based on opinion and therefore not well-defined. Empty Set- also referred to as the null set, this set contains no elements. Ex. {Unicorns on Earth} = probably an empty set. Statement- assertion of truth. Set-Builder Notation:  Set Braces { }, enclose the elements a set contains. Ex. {1,2,3,4}  Ellipsis points (…) , indicate that the set continues following the same pattern; can also indicate that the set is infinite if appearing at the end of a set. Ex. {1,2,3,4,…}  Separating line, |, reads “so that” or “such that”; seen when using variables in the statement of a set. Ex. {x | x is a natural number between 1 and 4} Funtulis- MATH 105 Review Section 1: Real Numbers – 1/22/16 Real Numbers  Natural Numbers: {1,2,3,4,…}  Whole Numbers: {0,1,2,3,…} whole numbers include zero!  Integers: {…-3,-2,-1,0,1,2,3,…} integers include negative numbers!  Rational Numbers: {p/q | p is an integer, q is an integer that is not zero} rational numbers are fractions that do not have a denominator of zero!  Irrational Numbers: {…π, square roots, e} irrational numbers include repeating, non- terminating numbers that cannot be expressed as a ratio of integers! Subset- a set within a set. Ex. Natural numbers are a subset of whole numbers. Containment- an element of a set that is expressed as being contained by a set. Ex. 0 E {x | -1 ≤ x < 3} *Integers are a proper subset of Rationals (proper- lacking some elements)* Funtulis- MATH 105 **Empty set- { } or ; { }- a set containing an empty set; - a subset of every set (the empty, or null, set}** The union of two sets, A and B for example, is the set that contains all of the elements of both A and B. Ex. A = {1,2,3}, B = {2,3,7}, so {1,2,3} U {2,3,7} = {1,2,3,7} The intersection of two sets, A and B for example, is the set that includes the elements set A and set B have in common. Ex. A = {1,2,3}, B = {2,3,7}, so {1,2,3} ∩ {2,3,7} = {2,3} Disjoint Set- sets that have no elements in common. Ex. A = {1,2,3}, B = {4,5,6}, therefore A ∩ B =


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