I get the definition of limit superior and limit inferior, but I can't start a proof for these properties:

Hope you may enlight me. :D

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- Mar 24th 2011, 02:04 PMConnectedLimit superior and limit inferior
I get the definition of limit superior and limit inferior, but I can't start a proof for these properties:

Hope you may enlight me. :D - Mar 24th 2011, 02:06 PMgirdav
Did you try to use the properties of and ?

- Mar 24th 2011, 02:37 PMConnected
Oh, not really.

How would you prove the third one? Can you show me?

Thanks! - Mar 24th 2011, 02:46 PMgirdav
Use for the first inequality. For the second, you have to show that . But .

- Mar 25th 2011, 01:50 PMConnected
So for the first one I use by taking limits I get the result. Is it correct?

The second one follows easily from right? - Mar 25th 2011, 01:53 PMgirdav
You have to tell where you take the . The definition is .

- Mar 25th 2011, 01:56 PMConnected
Oh well, so I need to add that to what I wrote.

But by adding this, is it correct? If not, how to do it?