1 / 102

MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets

MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets. For example: the set of seasons S = {Spring, Summer, Fall, Winter}. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets.

nomlanga-horn
Download Presentation

MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets

  2. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets For example: the set of seasons S= {Spring, Summer, Fall, Winter}

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

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

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

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

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

  9. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets For example: the set of seasons S= {Spring, Summer, Fall, Winter} 3 1 2 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. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets For example: the set of seasons S= {Spring, Summer, Fall, Winter} 3 1 2 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. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets More examples of sets:

  12. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets More examples of sets: T = {1, 2, 3, 4, 5}

  13. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets More examples of sets: T = {1, 2, 3, 4, 5} U = {1, 2, 3, … , 1000}

  14. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets More examples of sets: T = {1, 2, 3, 4, 5} U = {1, 2, 3, … , 1000} V = {1, 2, 3, 4, …}

  15. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  17. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  18. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  19. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  20. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  21. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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}

  22. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets

  23. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets A = {1, 2, 3, 4, 5} WELL DEFINED B= {x : x is tall} NOT WELL DEFINED

  24. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets A = {1, 2, 3, 4, 5} WELL DEFINED B= {x : x is tall} NOT WELL DEFINED

  25. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets A = {1, 2, 3, 4, 5} WELL DEFINED B= {x : x is tall} NOT WELL DEFINED

  26. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets A = {1, 2, 3, 4, 5} WELL DEFINED B= {x : x is tall} NOT WELL DEFINED

  27. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Є is the symbol for “is an element of”

  28. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets

  32. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Let M = {x: x is a female U.S. President before 2010}

  33. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets

  36. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Ifyouarechoosinga3-personcommitteefroma50member club,theUniversalsetconsistsofthenamesofall50members.

  37. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Ifyouarechoosinga3-personcommitteefroma50member club,theUniversalsetconsistsofthenamesofall50members. 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. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Ifyouarechoosinga3-personcommitteefroma50member club,theUniversalsetconsistsofthenamesofall50members. 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 getU = {0, 1, 2}.

  39. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets Ifyouarechoosinga3-personcommitteefroma50member club,theUniversalsetconsistsofthenamesofall50members. 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 getU = {0, 1, 2}.

  40. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets THE UNIVERSAL SET IS CONTEXTUAL…IT DEPENDS COMPLETELY ON THE CONTEXT OF THE PROBLEM.

  41. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets

  46. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets n(A) is read

  47. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets n(A) is read ‘the cardinal number of A’ or more informally, ‘the number of elements of A’.

  48. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets n(A) is read ‘the cardinal number of A’ or more informally, ‘the number of elements of A’.

  49. MATH 110 Sec 2-1 , 2-2 Lecture on Sets and Comparing Sets 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 , 2-2 Lecture on Sets and Comparing Sets 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.

More Related