Interval Notation: Clear Explanation

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    Interval Notation
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Discussion Overview

The discussion revolves around the concept of interval notation in mathematics, focusing on its definitions and interpretations. Participants seek clarity on how to express intervals using different notations and the implications of including or excluding endpoints.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about interval notation and requests a clear description.
  • Another participant suggests a Wikipedia link for reference and asks for specifics on what is unclear.
  • A third participant provides a link to a resource on set notation, indicating that understanding set notation is essential for grasping interval notation.
  • Multiple participants explain the meanings of different interval notations, such as (a, b), [a, b), (a, b], and [a, b], detailing which endpoints are included or excluded.
  • One participant emphasizes that all these notations represent the interval between a and b, highlighting the significance of brackets and parentheses in denoting inclusivity of endpoints.
  • There is a mention of "HOI" being interpreted as (a, b], although it is unclear if this is a widely accepted notation.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of the interval notations, but there is some contention regarding the clarity and helpfulness of external resources. The discussion remains unresolved regarding the best way to convey the concept to the original poster.

Contextual Notes

Some participants note the importance of understanding set notation as a prerequisite for grasping interval notation, but the specific assumptions or prior knowledge of the original poster are not fully clarified.

science~life
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Can anyone please give a succinct and clear description on this? I'm a little confused...
 
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http://www.purplemath.com/modules/setnotn.htm

Set notation. This will help you read the wiki article.

Need to know where you at with it to be able to help.

Do you understand (a, b] means a isn't included in the interval but b is?
 
(a, b) means "all numbers strictly between a and b". It can also be written as [itex]\{x| a< x< b\}[/itex].

[a, b) means "all numbers strictly between a and b and the number a. It can also be written as [itex]\{x| a\le x< b\}[/itex].

(a, b) means "all numbers strictly between a and b and the number b. It can also be written as [itex]\{ x| a< x\le b\}[/itex].

[a, b] means "all numbers strictlhy between a and b and both the number a and the number b. It can also be written as [itex]\{x| a\le x\le b\}[/itex].

In short, all of these contain the interval between a and b. "[" and "]" mean "include this end point". "(" and ")" mean "do not include this point".
 
HallsofIvy said:
(a, b) means "all numbers strictly between a and b". It can also be written as [itex]\{x| a< x< b\}[/itex].

[a, b) means "all numbers strictly between a and b and the number a. It can also be written as [itex]\{x| a\le x< b\}[/itex].

(a, b) means "all numbers strictly between a and b and the number b. It can also be written as [itex]\{ x| a< x\le b\}[/itex].

[a, b] means "all numbers strictlhy between a and b and both the number a and the number b. It can also be written as [itex]\{x| a\le x\le b\}[/itex].

In short, all of these contain the interval between a and b. "[" and "]" mean "include this end point". "(" and ")" mean "do not include this point".

Third, HOI certainly means (a,b], just in case this is not caught.
 

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