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Theoreticals of Calculus: could someone explain indexed family of sets to me??
 one year ago
 one year ago
Theoreticals of Calculus: could someone explain indexed family of sets to me??
 one year ago
 one year ago

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

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

KingGeorgeBest ResponseYou've already chosen the best response.1
Well, 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.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
And can you be a little more specific on what parts about the intersection are confusing you?
 one year ago

manjuthottamBest ResponseYou've already chosen the best response.0
oh 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?
 one year ago

manjuthottamBest ResponseYou've already chosen the best response.0
i thought the answer would be 1 as well
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Ah. 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 \(1<x<2\).
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You 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.
 one year ago

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

manjuthottamBest ResponseYou've already chosen the best response.0
that makes sense thank you!!
 one year ago
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