101 - Set Concepts and Naming Sets

7/31/2019 101 - Set Concepts and Naming Sets

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Basic Terms and Concept

Naming Sets


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A set is a well-defined

collection of objects which

are called elements ormembers. A well

defined set is a set whoseelements can clearly bedetermined.


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WELL DEFINED SET:

The set of members of one

direction

NOT WELL DEFINED:SET OF BEST BAND


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WELL DEFINED SET:

The set of months in a year

NOT WELL DEFINED:

The hottest months of theyear


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Sets are named using

capital letters.

Ellipsis () are used only ifthere is a clear pattern of

elements in a set and thatsome of these elements are

not shown or written.


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O = { 1, 3, 5, 7, 9}

E = {2, 4, 6, 8, 10, 20}W = {1, 2, 3, 4, 5, 6, }


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The elements of a set are

the distinct members

included in the discussion.


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A = {1, 4, 9, 16, 25 }

B = {1, 2, 3, 5, 8, 13, 21}

A4 A2

B21 B14


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The cardinality of a setrefers to the number of

elements in a set.

)(An


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A = {1, 4, 9, 16, 25 }

B = {1, 2, 3, 5, 8, 13, 21}7)( Bn

What is n(A)?


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Universal set refers to theset which contains all the

elements under discussion.

U


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U = {all counting numbers}

U = {all odd numbers}U = {all even numbers}

U = {all positive integers}


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Subsets are sets that areformed from some or all

elements of a given set.

BA AB


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ABU


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U = {all odd numbers}

C = {1, 3, 5}

D = {99, 101, 103}


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C = {1, 3, 5}

What are the subset of set C?How many subsets did you

form?

Is it possible to determine thenumber of subsets whose

cardinality is infinite?


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C = {1, 3, 5}

Is it possible to make a subsetthat contains all the elements

of the original set?

Is it possible to make a subsetthat has no elements?


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n

2n is the number of elements in

the given set


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E = {January, February, March,

.December}

Is it a well defined set?

Can you give two elements of set E?

What is the n (E)?Can you give one subset of set E?

How do you describe set E?


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enumerating the elements

of a set inside a pair ofbraces.

Example:Y= {January, February,MarchDecember}


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describing the common

property of the elements in aset without enumerating the

elements.Example:Y is the set of months in a year.


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Often used in higher

mathematics courses and is

easier to understand and moreconvenient to use since it is

concise.Example:Y = { x | x is a month in a year}


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[Journal]:

Write 3 important points that

you learned about todaystopic.

101 - Set Concepts and Naming Sets

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