What Are Examples of Discontinuous Functions and Their Properties?

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Homework Help Overview

The discussion revolves around examples of discontinuous functions and their properties, including specific inquiries about piecewise functions, nested sequences of non-compact sets, and unbounded infinite sets without accumulation points.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to provide examples of discontinuous functions and questions the validity of their reasoning regarding the piecewise function. They also explore the concept of accumulation points in relation to specific sets.

Discussion Status

Some participants express a reluctance to provide direct answers, emphasizing the forum's policy against doing homework for users. The original poster indicates they have invested time in understanding the problems and seeks constructive guidance rather than straightforward solutions.

Contextual Notes

There is a mention of previous unanswered threads, suggesting a concern about the responsiveness of the forum. The original poster acknowledges their understanding of basic theorems but seeks further clarification and support.

Kraziethuy
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1. An example of a discontinuous function on an interval [a,b] that does not assume every value between f(a) and f(b).

[edit] My answer to this: Piecewise function f(x)= 1/x, for x greater than and equal to -4 but less than zero (0). And f(x)=1/x for x greater than zero but less than and equal to 4. This makes the function discontinuous, on the interval [-4,4]. Now, I let c=0. There does not exist a value x in (-4,4) such that f(x)=c. Correct?

2. Find a nested sequence of non-compact sets whose intersection is empty.

3. An example of an unbounded infinite set that has no accumulation point.

For this one, I know that 1/n, for n=1,2,3,... has ONLY zero as an accumulation point, so can I maybe do something like {1/n}U{0} so that there is no longer an accumulation point? I'm pretty suck on this one.

[edit] (I figured out #4 and #5 now o:) )
 
Last edited:
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we won't do HW for you, read the sticky

https://www.physicsforums.com/showthread.php?t=4825
 
My other thread went unanswered for the most part, and I'd rather not explain this one if it's going to end up the same way. If I made it this far in math, it's obviously not because I don't do my own hw.

I've spent two days already working with these problems and the other two listed in my previous thread. I know the basic theorems used in deciphering the problems, but haven't built up anything to go along with what I've posted.

I know it looks as though I'm just going for a quick answer, but even then I'd have to prove the answer received anyway. So there aren't free answers here.
 
I'm just here for help. If you don't want to help, then please don't reply.
 

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