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College Math - Set Builder Notation

express the following in set builder notation: Z = {13,14,15,16,17,18,19,20,21}

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Sep 24, 2011
Set Builder Notation
by: Staff

The question:

epress the following in set builder notation: Z = {13,14,15,16,17,18,19,20,21}

The answer:

Four different ways of representing set Z are shown below:

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

1. ROSTER Notation:

Z = {13,14,15,16,17,18,19,20,21}

2. SET BUILDER Notation:

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

Here is a commonly used format:

Z = {n | n ∈ ℕ, 13 ≤ n ≤ 21}

{} curly brackets surround the expression
∈ = element of a set

| and : can be used interchangeably. Both notations are separators which mean "where" or "such that"

n: the first "n" is the "output function", shown as = {n |

n: the second "n" is the "variable", shown as | n ∈ N,

ℕ (the set of all natural numbers) is the "input set"

13 ≤ n ≤ 21 is the "predicate"

Reading from left to right: "Z" is the set of all numbers "n" {n | ... , ...} where "n" is an element of the set of natural numbers ℕ { ... | n ∈ ℕ, ... } and "n" is greater than or equal to 13 and less than or equal to 21 {... | ... , 13 ≤ n ≤ 21}.

3. INTERVAL Notation:

This is a "closed interval". The endpoints of 13 and 21 "are included" in the interval. Therefore [ ] must be used to show the interval.

However, this notation CANNOT BE USED: Z = [13, 21]. [13, 21] means all REAL numbers between from 13 through 21 (including endpoints)

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

Interval Notation for Integers should be written:

Z = [13 . . 21]

It should be read: the set of all integers beginning with (and including) 13 and ending with (and including) 21.

4. GRAPHICAL Representation:

Z = {13,14,15,16,17,18,19,20,21}

Open the link shown below to view the graphical representation of set Z:

(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:


Thanks for writing.


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