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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.

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

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  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.

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