71 basic languages of sets

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71 basic languages of sets

  1. 1. The Basic Language of Sets
  2. 2. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).
  3. 3. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.
  4. 4. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”,
  5. 5. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}.
  6. 6. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.
  7. 7. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M
  8. 8. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M and similarlyy ϵ M means that y is not an element in M.
  9. 9. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M and similarlyy ϵ M means that y is not an element in M.Hence p ϵ M but King Kong ϵ M.
  10. 10. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M and similarlyy ϵ M means that y is not an element in M.Hence p ϵ M but King Kong ϵ M.An element may be listed once only.
  11. 11. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M and similarlyy ϵ M means that y is not an element in M.Hence p ϵ M but King Kong ϵ M.An element may be listed once only. If Maria has two quarters inthe purse, then we must list M as {p, d, q1, q2}.
  12. 12. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M and similarlyy ϵ M means that y is not an element in M.Hence p ϵ M but King Kong ϵ M.An element may be listed once only. If Maria has two quarters inthe purse, then we must list M as {p, d, q1, q2}.If we are to list the setT = {different types of coins in Maria’s purse},
  13. 13. The Basic Language of SetsA set in mathematics is a collection of items (real or abstract).A set may be given by a description or we may list the items ofthe set in a “{ }”.For example, we may define the set M to be“the coins in Maria’s purse”, and if Maria’s purse containsexactly a penny, a dime and a quarter, then we may list M as{p, d, q}. Each item in the set M is called an element of M.If x is an element of the set M, we write that x ϵ M.Similarly y ϵ M means that y is not an element in M.Hence p ϵ M but King Kong ϵ M.An element may be listed once only. If Maria has two quarters inthe purse, then we must list M as {p, d, q1, q2}.If we are to list the setT = {different types of coins in Maria’s purse},then T = {P, Q, D} where P, Q, and D represent the types of thecoins regardless M = {p, d, q} or {p, d, q1, q2}.
  14. 14. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).
  15. 15. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.
  16. 16. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.
  17. 17. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.
  18. 18. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A.
  19. 19. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite.
  20. 20. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞.
  21. 21. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite.
  22. 22. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem.
  23. 23. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem. Every time we list one number, there is the next oneinline to be listed.
  24. 24. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem. Every time we list one number, there is the next oneinline to be listed. Hence o(N) = ∞.
  25. 25. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem. Every time we list one number, there is the next oneinline to be listed. Hence o(N) = ∞.Sets related to geometry are often defined by inequalities anddrawn with pictures.
  26. 26. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φand that o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem. Every time we list one number, there is the next oneinline to be listed. Hence o(N) = ∞.Sets related to geometry are often defined by inequalities anddrawn with pictures. For example,if K = {x | 0 < x < 2} or {x : 0 < x < 2}, “ such that”
  27. 27. The Basic Language of SetsThe number of elements in the set A is called the order of Aand it’s denoted as o(A).If M = {p, d, q}, then o(M) = 3.If M = {p, d, q1, q2}, then o(M) = 4.The empty set { } which contains nothing is denoted as Φ;therefore o(Φ) = 0.A set A is said to be finite if o(A) is finite, i.e. we can finishcounting all the items in A. A set that is not finite is said to beinfinite. If B is infinite, we write that o(B) = ∞. The set of naturalnumbers N = {1, 2, 3,…} is not finite. We can not finish listingthem. Every time we list one number, there is the next oneinline to be listed. Hence o(N) = ∞.Sets related to geometry are often defined by inequalities anddrawn with pictures. For example, 0 x 2if K = {x | 0 < x < 2} or {x : 0 < x < 2}, The set Kthen o(K) is also ∞ and K can be drawn as shown.
  28. 28. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).
  29. 29. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.
  30. 30. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).
  31. 31. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).R = {a, b, d} and that o(R) = 3.
  32. 32. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).R = {a, b, d} and that o(R) = 3.c. Let N = {non–adult(s) that is wearing something green}.List N and find o(N).
  33. 33. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).R = {a, b, d} and that o(R) = 3.c. Let N = {non–adult(s) that is wearing something green}.List N and find o(N).N = {c} and that o(N) = 1.
  34. 34. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).R = {a, b, d} and that o(R) = 3.c. Let N = {non–adult(s) that is wearing something green}.List N and find o(N).N = {c} and that o(N) = 1.d. List T = {members that are not wearing shoes} and find o(T).
  35. 35. The Basic Language of SetsExample A. Farmer Andy’s familyGiven a photo of Farmer Andy’sfamily, answer the followingquestions. Andy Beth Cathy Dana. Let U be the set of Farmer Andy’sfamily members. List U and find o(U).Using the 1st letter of their names, we may express FarmerAndy’s family as U = {a, b, c, d} and that o(U) = 4.b. Let R be the set of members that are wearing somethingred. List R find o(R).R = {a, b, d} and that o(R) = 3.c. Let N = {non–adult(s) that is wearing something green}.List N and find o(N).N = {c} and that o(N) = 1.d. List T = {members that are not wearing shoes} and find o(T).Everyone is wearing shoes, so T = Φ = { } and that o(T) = 0.
  36. 36. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set. Andy Beth Cathy Dan
  37. 37. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set.The universal set U is the same Andy Beth Cathy Danas “the population” in Statistics which describe the entire setof objects under the study.
  38. 38. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set.The universal set U is the same Andy Beth Cathy Danas “the population” in Statistics which describe the entire setof objects under the study. Hence if Farmer Andy’s family isour sole interest, then the universal set U, or the population,is {a, b, c, d}.
  39. 39. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set.The universal set U is the same Andy Beth Cathy Danas “the population” in Statistics which describe the entire setof objects under the study. Hence if Farmer Andy’s family isour sole interest, then the universal set U, or the population,is {a, b, c, d}. UGiven two sets A and U, we say that AA is a subset of U, and we write thatA B, if every element in A is also in U. ∩ A U ∩
  40. 40. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set.The universal set U is the same Andy Beth Cathy Danas “the population” in Statistics which describe the entire setof objects under the study. Hence if Farmer Andy’s family isour sole interest, then the universal set U, or the population,is {a, b, c, d}. UGiven two sets A and U, we say that AA is a subset of U, and we write thatA B, if every element in A is also in U. ∩If A U but A ≠ B, i.e. U contains element(s) A U ∩ ∩besides the ones in A, then we say that A is a proper subsetof B and we write that A U. ∩
  41. 41. The Basic Language of SetsIn mathematics, the set U that Farmer Andy’s familyholds all the elements is calledthe universal set.The universal set U is the same Andy Beth Cathy Danas “the population” in Statistics which describe the entire setof objects under the study. Hence if Farmer Andy’s family isour sole interest, then the universal set U, or the population,is {a, b, c, d}. UGiven two sets A and U, we say that AA is a subset of U, and we write thatA U, if every element in A is also in U. ∩If A U but A ≠ B, i.e. U contains element(s) A U ∩ ∩besides the ones in A, then we say that A is a proper subsetof B and we write that A U. ∩Given two finite sets A and B,if A B then o(A) ≤ o(B), if A B then o(A) < o(B). ∩ ∩
  42. 42. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ Andy Beth Cathy Dan
  43. 43. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy Dan
  44. 44. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩
  45. 45. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.
  46. 46. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.Subsets of U extracted with specific attributes are calledsample sets or samples.
  47. 47. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.Subsets of U extracted with specific attributes are calledsample sets or samples. For example the setA = {all adult American} is a sample set from U.
  48. 48. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.Subsets of U extracted with specific attributes are calledsample sets or samples. For example the setA = {all adult American} is a sample set from U. Sample setsmay also be selected randomly.
  49. 49. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.Subsets of U extracted with specific attributes are calledsample sets or samples. For example the setA = {all adult American} is a sample set from U. Sample setsmay also be selected randomly. A random sample S of size 25would be a subset of 25 elements selected randomly from U.
  50. 50. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all American}.Subsets of U extracted with specific attributes are calledsample sets or samples. For example the setA = {all adult American} is a sample set from U. Sample setsmay also be selected randomly. A random sample S of size 25would be a subset of 25 elements selected randomly from U.Example B. List all the possible sample sets of size 2 fromFarmers Fred’s family U.
  51. 51. The Basic Language of SetsHence R = {a, b, d} Farmer Andy’s familyis a proper subset ofU = {a, b, c, d}, or R U. ∩ ∩Also the set N = {c} U. Andy Beth Cathy DanNote that “{c} U” and “c ϵ U” have different meanings. ∩and that “{c} ϵ U” and “c U” do not make sense. ∩It we wish to study the fast food habit of Americans,then the population of the study is U = {all Americans}.Subsets of U extracted with specific attributes are calledsample sets or samples. For example the setA = {all adult Americans} is a sample set from U. Sample setsmay also be selected randomly. A “random sample S of size 25”would be a subset of 25 elements selected randomly from U.Example B. List all the possible sample sets of size 2 fromFarmers Fred’s family U.There are six of them {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}.
  52. 52. The Basic Language of SetsSets come in 2 types; discrete and continuous.
  53. 53. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}.
  54. 54. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}.
  55. 55. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. We use the “…” to mean “to continue in the same manner”.
  56. 56. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. No matter how large anumber is, say 1,0001,000,000,
  57. 57. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. No matter how large anumber is, say 1,0001,000,000, if we start to list N orderly as{1, 2, 3,... }, we know that 1,0001,000,000 would appear down theline.
  58. 58. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. No matter how large anumber is, say 1,0001,000,000, if we start to list N orderly as{1, 2, 3,... }, we know that 1,0001,000,000 would appear down theline. These listable sets are said to be discrete.
  59. 59. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. No matter how large anumber is, say 1,0001,000,000, if we start to list N orderly as{1, 2, 3,... }, we know that 1,0001,000,000 would appear down theline. These listable sets are said to be discrete.But the set K = {x | 0 < x < 2} 0 x 2which contains fractions ½, ¾ … and The set Kirrational numbers such as 0.123401..,√2,is an infinite set that is packed so tightly that there is no orderlymanner to list all these numbers–as we did for M or N.
  60. 60. The Basic Language of SetsSets come in 2 types; discrete and continuous.Recall that the set M = {coins in Maria’s purse} may be listedexplicitly as {p, d, q}. A finite set may always be listedcompletely as {x1, x2, .., xn}. The set of natural numbersN = {1, 2, 3,…} may also be listed in the sense that everynatural number appears in this list. No matter how large anumber is, say 1,0001,000,000, if we start to list N orderly as{1, 2, 3,... }, we know that 1,0001,000,000 would appear down theline. These listable sets are said to be discrete.But the set K = {x | 0 < x < 2}, 0 x 2which contains fractions ½, ¾ … and The set Kirrational numbers such as 0.123401..,√2,is an infinite set that is packed so tightly that there is no orderlymanner to list all these numbers–as we did for M or N.A set such as K whose elements may be packed into intervalsare said to be continuous.
  61. 61. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.
  62. 62. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?
  63. 63. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?Since the number of eggs n could be {0, 1, 2,... } from adiscrete set, hence the sample data is discrete
  64. 64. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?Since the number of eggs n could be {0, 1, 2,... } from adiscrete set, hence the sample data is discreteb. Farmer Andy is interested in studying the health of the appletrees by randomly selecting an apple daily and measure itsweight w, is this type of data discrete or continuous?
  65. 65. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?Since the number of eggs n could be {0, 1, 2,... } from adiscrete set, hence the sample data is discreteb. Farmer Andy is interested in studying the health of the appletrees by randomly selecting an apple daily and measure itsweight w, is this type of data discrete or continuous?This type of data is continuous because w could be anywherebetween 0 up to, say, 2 lb, i.e. w ϵ K = {w | 0 < w < 2}.
  66. 66. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?Since the number of eggs n could be {0, 1, 2,... } from adiscrete set, hence the sample data is discreteb. Farmer Andy is interested in studying the health of the appletrees by randomly selecting an apple daily and measure itsweight w, is this type of data discrete or continuous?This type of data is continuous because w could be anywherebetween 0 up to, say, 2 lb, i.e. w ϵ K = {w | 0 < w < 2}.The elements in a discrete set may be line up and counted likesheep.
  67. 67. The Basic Language of SetsSimilarly in Statistics, sample sets are classified as discrete orcontinuous accordingly.Example C. a. Farmer Andy is interested in studying the eggs nthat he found daily, is this type of data discrete or continuous?Since the number of eggs n could be {0, 1, 2,... } from adiscrete set, hence the sample data is discreteb. Farmer Andy is interested in studying the health of the appletrees by randomly selecting an apple daily and measure itsweight w, is this type of data discrete or continuous?This type of data is continuous because w could be anywherebetween 0 up to, say, 2 lb, i.e. w ϵ K = {w | 0 < w < 2}.The elements in a discrete set may be line up and counted likesheep. The elements in a continuous set I are packed so tightlyinto an interval(s) that there is no way to separate and line up allthe numbers in I. Physical measurements such as length andweight which may be measured to any precision are continuous.

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