A community for students.
Here's the question you clicked on:
 0 viewing
manjuthottam
 2 years ago
Theoreticals of Calculus: could someone explain indexed family of sets to me??
manjuthottam
 2 years ago
Theoreticals of Calculus: could someone explain indexed family of sets to me??

This Question is Closed

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0Here is a pdf of a question and solution involving indexed family sets on page 5 & 6! please and thankyou!!

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0is there a difference between {} and [] ? Also I am making more mistake on finding the intersection portion of the set

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Well, whenever you see { and }, those denote generic sets. In this case, [ and ] are denoting an interval on the real number line. So [1,2] is just every real number \(x\) such that \(1\le x\le2\). So if you have \[\left\{\left[1,1+\frac{1}{n}\right]:n\in\mathbb{N}\right\},\] this is the set of all intervals \([1,1+1/n]\) such that \(n\) is a natural number greater than 0.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1And can you be a little more specific on what parts about the intersection are confusing you?

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0oh ok i understand now about the {} and[]! about the intersection, on page 5 the intersection is {1} but why on page 7 the intersection is empty set?

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0i thought the answer would be 1 as well

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Ah. On page 7, they use ( and ) instead of [ and ]. The difference between these two, is whether the endpoints are included. So if you have [1,2], this is every real number x such that \(1\le x\le2\). However, (1,2) is every real number x such that \(1<x<2\).

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1You can also mix and match. So (1,2] would be all real numbers x such that \(1<x\le2\). All in all, on page 7, you have an empty intersection because 1 is never included in any of the sets.

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0oh so since < > are used, 1 is not part of the set, just the smallest number slightly greater than it is?

manjuthottam
 2 years ago
Best ResponseYou've already chosen the best response.0that makes sense thank you!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.