Download presentation

Presentation is loading. Please wait.

Published byMarianna Williams Modified over 4 years ago

1
The Language of Sets MATH 102 Contemporary Math S. Rook

2
Overview Section 2.1 in the textbook: – Representing sets – More with sets

3
Representing Sets

4
4 Sets Set: a collection of objects. Each object is known as a member or an element of the set – We usually use capital letters to denote sets and lowercase letters to denote elements of sets Two ways to express sets: – Set-Builder notation – Roster notation

5
5 Set-Builder Notation Set-Builder Notation: describes, but does not explicitly list the elements of a set e.g. {x | x is an even number}, The | (vertical bar) is pronounced “such that” e.g. is pronounced “is an element of the set of”

6
6 Roster Notation Roster Notation means to explicitly list the elements of a set – When listing elements, we use set notation and place the elements between and left { and right } (called curly braces) – We use … (ellipses) to denote a set extending infinitely in the same pattern The set of even numbers can then be expressed as {0, 2, 4, 6, …} How can we express {x | x ε odd number} in roster notation?

7
7 Common Sets of Numbers Sets of numbers to be familiar with: – Natural numbers (counting numbers): {1, 2, 3, 4, 5,…} {x | x ε N} – Whole numbers: the natural numbers along with 0. {0, 1, 2, 3, 4,…} {x | x ε W} – Integers: the natural numbers, opposite of the natural numbers, and zero. {…, -2, -1, 0, 1, 2,…} {x | x ε I}

8
8 Common Sets of Numbers (Continued) – Rational numbers: any number that can be expressed as the quotient of two integers, a, b, b ≠ 0. { a ⁄ b | a and b are integers, b ≠ 0} {x | x ε Q} – Real numbers: any number that lies on the number line {x | x ε R}

9
Converting Between Roster & Set- Builder Notation (Example) Ex 1: Convert to roster notation: a) b) A = {y | y is a letter in the word music} 9

10
Converting Between Roster & Set- Builder Notation (Example) Ex 2: Convert to set-builder notation: a) C = {-5, -4, -3, -2, -1} b) D = {…, -2, -1, 0, 1, 2, 3, 4} 10

11
More with Sets

12
Null/Empty Set Null/Empty Set: a set that contains NO elements – Represented as { } or Ø – What would be an example of an empty set written in set-builder notation? Does { } have same meaning as {Ø}? – Think of the curly braces as a container/bag – See pg 41 in the textbook

13
Set Membership Recall that we use the symbol to denote an element that can be found within a set MUST be careful on precise usage: – Is the statement 1 ε {1, 2, 3} true? – Is the statement {1} ε {1, 2, 3} true? – Is the statement {2} ε { {1}, {2}, {3} } true? – Is the statement {2} ε { {1, 2}, {3} } true? – Is the statement 1 ε { {1}, 2, 3} true? – Is the statement Ø ε {Ø} true? – Is the statement Ø ε {1, 2, 3} true?

14
Set Membership (Example) Ex 3: Replace # with to make the statement true: a)3 # {x | x is a whole number} b)Tiger Woods # {a | a is a professional ice skater} c){1, 5} # { {1}, {5}, {1, 5} } d)0 # Ø e)Ø # {0}

15
Cardinal Number of a Set Cardinal number: the number of elements in a set A denoted by n(A) – Sets that have a countable number of elements are called finite – Sets that have a number of elements that are not countable are infinite

16
Cardinal Number of a Set (Example) Ex 4: Identify the set as finite or infinite. If finite, list the cardinal number of the set. a)A = Ø b)B = { …, -10, -9, -8, -7, -6} c)C = { {2, 3, 5}, {7, 11}, {13, 17, 19} } d) D = {d | d is a person in this class today} e)E = {e | e is a digit in π}

17
Summary After studying these slides, you should know how to do the following: – Express the elements of a set in set-builder or roster notation – Understand the concept of the null/empty set – State whether a given element is a member of a set – Classify sets as finite or infinite – Find the cardinal number of a finite set Additional Practice: – See the list of suggested problems for 2.1 Next Lesson: – Comparing Sets (Section 2.2)

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google