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Set Notation - Integers Less than 12

by Mike
(Burlington, Canada, Ontario)











































Representing an Integer Set

Four different ways of representing a set are:

1. ROSTER Notation
2. SET BUILDER Notation
3. INTERVAL Notation
4. GRAPHICAL Representation

{x|x is a positive integer less than 12}

(Hint: 0 is considered a positive integer)

Comments for Set Notation - Integers Less than 12

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Feb 03, 2013
Integer Set
by: Staff


Answer

Part I


1. ROSTER Notation:

A roster notation is a list of all the elements in the set. Elements are separated from one another by commas. The entire set is enclosed by curly brackets (also called braces).

Set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}



2. SET BUILDER Notation:

Set-builder notation does not list all the elements of a set the way roster notation does. Instead, set-builder notation describes the properties of the elements of the set.

There is more than one format for writing this sequence in Set Builder Notation.


Here is a commonly used format:


Set A = {x | x ∈ ℤ, 0 ≤ x < 12}


x: the first “x” is the “output function”, shown as = {x |

x: the second “x” is the “variable”, shown as | x ∈ ℤ

| and : can be used interchangeably. Both notations are separators which mean “where” or “such that”. To type │, hold down the "alt" key, type 179, and then release the alt key.

∈, element of a set. To type, hold down the "alt" key, type 8712, and then release the alt key.

ℤ, (the set of all INTEGERS, represented as a "Double Z") is the "input set”. To type ℤ, hold down the "alt" key, type 8484, and then release the alt key.

0 ≤ x < 12 is the “predicate”. To type ≤, hold down the "alt" key, type 8804, and then release the alt key.


Set A = {x | x ∈ ℤ, 0 ≤ x < 12}

Reading from left to right: “Set A” is the set of all numbers “x” {x | … , …} where “x” is an element of the set of integers ℤ { … | x ∈ ℤ, … } and “x” is greater than or equal to 0 and less than 12 {… | … , 0 ≤ x < 12}.


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Feb 03, 2013
Integer Set
by: Staff


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Part II


3. INTERVAL Notation:

The interval notation describes a set differently than either the roster notation or the set-builder notation. The interval notation lists the number at each end of the set (low and high). The set consists all the numbers which lie between the two end points.

If the lower end point number is to be included in the set, it is preceded by a "[" . If the lower end point is not included in the set, it is preceded by a "(" .

If the upper end point number is included in the set, it is followed by a "]" . If the upper end point is not included in the set, it is followed by a ")" .

The interval notation for the set described in the problem statement is:

Set A = [0 . . 12)

This is classified as a "left closed, right open" interval. The integer 0 is included in the set, but the number 12 is not.

Your set includes only INTEGERS. Your set does not include any other real numbers.

The notation ". ." indicates that the set is a set of integers.


Interval Notation for Integers should be written:

Set A = [0 . . 12)


It should be read: the set of all integers beginning with (and including) 0 and ending with (and excluding) 12.



4. GRAPHICAL Representation:

Set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Math – graph interval on a number line








Thanks for writing.

Staff
www.solving-math-problems.com


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