2.1 Set Concepts Flashcards
Set
Collection of objects (ex: United States)
Elements β
The objects in a set (ex: the 50 states of the United States)
β meaning βelement ofβ
Well-defined
Contents can clearly be determined (ex: set of US)
Not well-defined
Contents cannot be clearly determined (ex: the best movies on Netflix)
What are the 3 methods used to indicate a set?
Description, roster form, set-builder notation
Description
Ex: Write a description of the set containing Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
Roster form
List the elements of a set inside a pair of brackets (ex: {1, 2, 3, 4,β¦, 10})
Set-builder notation
Used to symbolize a set (ex: E = {π₯|π₯ β π πππ π₯ > 10})
Inclusive
Includes the numbers stated in roster form (ex: set of natural numbers between 5 and 20 inclusive is {5, 6, 7, 8, β¦, 20})
Finite
Either contains no elements or the number of elements in the set is a natural number (the set ends)
Infinite
The set is not finite (ex: {1, 2, 3, β¦})
How can two sets be equal?
If they contain elements that are exactly the same, regardless of order (ex: {2, 4, 6} = {4, 2, 6})
How can two sets be equivalent?
If both setsβ cardinal numbers are the same (ex: {1, 2, 3} is equivalent to {red, yellow, orange})
Cardinal number π(π΄)
The number of elements in a set
One-to-one correspondence
Every element of set A can be matched with exactly one element set B
