Attachment 28246

I really need to get help for this problem. I'm learning continuous inverse theorem, uniformly continuous, Bolzano intermediate values theorem, and so on.

Thank you!

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- May 4th 2013, 10:29 PMtherexistsReal Analysis Please Help
Attachment 28246

I really need to get help for this problem. I'm learning continuous inverse theorem, uniformly continuous, Bolzano intermediate values theorem, and so on.

Thank you! - May 5th 2013, 05:42 AMPlatoRe: Real Analysis Please Help
It is difficult to help because we don't know how the definitions or theorems work.

How do your notes define*jump*? I have seen it defined exactly as what you are asked to prove.

Have you proved that if $\displaystyle f$ is increasing on open interval $\displaystyle I$ then $\displaystyle f(x-)~\&~f(x+)$ (the left-hand limit and the right-hand limit) exist for $\displaystyle \forall x\in I~?$

If you have that theorem then apply it to this problem.

If not, try to prove it. Or post the theorems and definitions you have to use. - May 5th 2013, 06:45 AMtherexistsRe: Real Analysis Please Help
I had to post with def and thm! But I really thank you for caring my post.

I will repost it with def and thm. I hope you will check this again.

Thanks again! - May 5th 2013, 06:53 AMProve ItRe: Real Analysis Please Help
Bean Interval:

https://a248.e.akamai.net/f/248/1856.../mqdefault.jpg