University:
Boston University
Course:
CAS MA 411 | Advanced Calculus
Academic year:

2021
Views:

387

Pages:

13
Author:

Salvador Meadows

Let‟s Begin with an Activity Ita and Kim eat croissants every morning Ita Kim Kim, Ita and Kate love Artemis! Kate • Partner up with 2 of your neighbors • Find out your similarities and differences. (Do you all like chocolate ice cream? Have you read Harry Potter? Etc…) • Fill in each section of the Venn Diagram What is a Set? A set is a collection of distinct objects. Example: {Book, Chair, Pen} In a set, order does not matter Example: {Book, Chair, Pen} = {Pen, Book, Chair} Your Venn Diagram is made of 3 sets of words describing you and your partners Two Important Sets Empty (Null) Set: A set with no elements Denoted by  or {} Universal Set: A set that contains all objects in the universe Denoted by Ω Elements The objects in a set are called “elements” Let S = {Emily, Kimerah, Katherine} Emily is said to be “an element of” set S because she is part of that set The shorthand notation for this is ‟∈‟ “Emily ∈ S” translates to “Emily is an element of set S” Basic Operations Union: The union of 2 sets is all the elements that are in both sets Denoted by „U‟ Example: Let A={1,2,3} and B={1,4,5} AUB = {1, 2, 3, 4, 5} Basic Operations Intersection: The intersection of 2 sets is the set of elements they have in common Denoted by „∩‟ Example: Let A={1,2,3} and B={1,4,5} A∩B = {1} Basic Operations Set Difference: The set of elements in one set and not the other Denoted by „\‟ Example: Let A={1,2,3} and B={1,4,5} A\B = {2, 3} Back to your Venn Diagram Identify … the union the intersection the set difference Solutions: Union Solutions: Intersection Solutions: Set Difference Why is Set Theory Important? It is a foundational tool in Mathematics The idea of grouping objects is really useful Examples: Complexity Theory: Branch in Comp. Sci. that focuses on classifying problems by difficulty. I.e. Problems are sorted into different sets based on how hard they are to solve The formal, mathematical definition of Probability is defined in terms of sets SET: The Game Rules Each card is unique in 4 characteristics: color, shape, number, and shading 3 cards form a SET if each characteristic is the same for all cards or different for all cards Yell SET to claim cards Player with the most SETs wins