1. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.

2. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}

3. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}
element
Each object is called an element of the set

4. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}
element
Each object is called an element of the set

5. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}
element
Each object is called an element of the set

6. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}
element
Each object is called an element of the set

7. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter}
There is a standard notation for indicating the number of elements in a set.

8. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter} 1 2 3 4
There is a standard notation for indicating the number of elements in a set.
The set S above has 4 elements

9. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter} 1 2 3 4
There is a standard notation for indicating the number of elements in a set.
The set S above has 4 elements
so we write

10. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
For example: the set of seasons S = {Spring, Summer, Fall, Winter} 1 2 3 4
There is a standard notation for indicating the number of elements in a set.
The set S above has 4 elements
so we write
n(S) = 4

11. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:

12. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}

13. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}

14. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}

15. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}

16. A set is a collection of objects.
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

17. W = {x : x is a 2 legged animal}
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

18. W = {x : x is a 2 legged animal}
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

19. W = {x : x is a 2 legged animal}
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

20. W = {x : x is a 2 legged animal}
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

21. W = {x : x is a 2 legged animal}
MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is a collection of objects.
More examples of sets:
T = {1, 2, 3, 4, 5}
U = {1, 2, 3, … , 1000}
V = {1, 2, 3, 4, …}
W = {x : x is a 2 legged animal}
W is written in what we call ‘set builder’ notation
Read as: “The set of all x, such that x is a 2 legged animal.”

22. MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is well defined if it is possible to definitively determine whether or not any particular object is a member of the set.

23. MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is well defined if it is possible to definitively determine whether or not any particular object is a member of the set.
A = {1, 2, 3, 4, 5} WELL DEFINED
B= {x : x is tall} NOT WELL DEFINED

24. MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is well defined if it is possible to definitively determine whether or not any particular object is a member of the set.
A = {1, 2, 3, 4, 5} WELL DEFINED
B= {x : x is tall} NOT WELL DEFINED

25. MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is well defined if it is possible to definitively determine whether or not any particular object is a member of the set.
A = {1, 2, 3, 4, 5} WELL DEFINED
B= {x : x is tall} NOT WELL DEFINED

26. MATH 110 Sec 2-1 Lecture on Intro to Sets
A set is well defined if it is possible to definitively determine whether or not any particular object is a member of the set.
A = {1, 2, 3, 4, 5} WELL DEFINED
B= {x : x is tall} NOT WELL DEFINED

27. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
Є is the symbol for “is an element of”

28. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
Є is the symbol for “is an element of”
If A = {1, 2, 3, 4, 5}, then 2 Є A.

29. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
Є is the symbol for “is an element of”
If A = {1, 2, 3, 4, 5}, then 2 Є A.
In general the symbol for “not” something is the symbol for that thing with a diagonal line through it.

30. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
Є is the symbol for “is an element of”
If A = {1, 2, 3, 4, 5}, then 2 Є A.
In general the symbol for “not” something is the symbol for that thing with a diagonal line through it.
For example, 7 ∉ A.

31. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set containing no elements is called the empty set (or sometimes, the null set).

32. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set containing no elements is called the empty set (or sometimes, the null set).
Let M = {x: x is a female U.S. President before 2010}

33. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set containing no elements is called the empty set (or sometimes, the null set).
Let M = {x: x is a female U.S. President before 2010}
Because this set is EMPTY, we can write

34. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set containing no elements is called the empty set (or sometimes, the null set).
Let M = {x: x is a female U.S. President before 2010}
Because this set is EMPTY, we can write
Ø or { }

35. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).

36. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
If you are choosing a 3-person committee from a 50 member club, the Universal set consists of the names of all 50 members.

37. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
If you are choosing a 3-person committee from a 50 member club, the Universal set consists of the names of all 50 members.
If you are looking at course grades in a class where the only grades possible are A, B, C, D, F, W, then U = { A, B, C, D, F, W}.

38. If you roll a die twice & count how many fives you get U = {0, 1, 2}.
MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
If you are choosing a 3-person committee from a 50 member club, the Universal set consists of the names of all 50 members.
If you are looking at course grades in a class where the only grades possible are A, B, C, D, F, W, then U = { A, B, C, D, F, W}.
If you roll a die twice & count how many fives you get U = {0, 1, 2}.

39. If you roll a die twice & count how many fives you get U = {0, 1, 2}.
MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
If you are choosing a 3-person committee from a 50 member club, the Universal set consists of the names of all 50 members.
If you are looking at course grades in a class where the only grades possible are A, B, C, D, F, W, then U = { A, B, C, D, F, W}.
If you roll a die twice & count how many fives you get U = {0, 1, 2}.

40. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.

41. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.
For example, if we are showing the results of a coin flip, U = { HEAD , TAIL }

42. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.
For example, if we are showing the results of a coin flip, U = { HEAD , TAIL }

43. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.
For example, if we are showing the results of a coin flip, U = { HEAD , TAIL }
If we roll a single ordinary die, then U =

44. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The set of all elements under consideration for a particular problem is called the universal set (U).
THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.
For example, if we are showing the results of a coin flip, U = { HEAD , TAIL }
If we roll a single ordinary die, then U = { 1 , 2 , 3 , 4 , 5 , 6 }

45. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.

46. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read

47. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.

48. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.

49. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
If A = { 1 , 2 , 4 , 6 , 8 , 10 }, then n(A) = 6.

50. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
A set is finite if its cardinal number is a whole number and infinite if its cardinal number is not a whole number.

51. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
A set is finite if its cardinal number is a whole number and infinite if its cardinal number is not a whole number.
A = { 1 , 2 , 4 }

52. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
A set is finite if its cardinal number is a whole number and infinite if its cardinal number is not a whole number.
A = { 1 , 2 , 4 }
FINITE

53. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
A set is finite if its cardinal number is a whole number and infinite if its cardinal number is not a whole number.
A = { 1 , 2 , 4 }
FINITE
A = { 2 , 4 , 6 , 8 , …}

54. MATH 110 Sec 2-1 Lecture on Intro to Sets
SYMBOLS
The number of elements in set A is called the cardinal number of the set.
n(A) is read
‘the cardinal number of A’ or more informally, ‘the number of elements of A’.
A set is finite if its cardinal number is a whole number and infinite if its cardinal number is not a whole number.
A = { 1 , 2 , 4 }
FINITE
A = { 2 , 4 , 6 , 8 , …}
INFINITE