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

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}

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

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

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

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

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.

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

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

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

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:

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}

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}

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, …}

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}

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.”

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.”

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.”

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.”

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.”

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.”

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.

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

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

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

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

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

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.

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.

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.

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).

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}

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

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 { }

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).

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.

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}. 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}.

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}.

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.

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 }

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 }

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 =

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 }

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.

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

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’.

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’.

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.

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.

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 }

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

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 , …}

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