i need to proove that lim inf(An*Bn)>=liminfAn * liminfBn

i got the opposite resolt

where is my mistake:

http://img187.imageshack.us/img187/6705/44112683ho1.gif

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- Jan 9th 2009, 04:14 AMtransgalacticwhere is my mistake in this liminf innquality proof
i need to proove that lim inf(An*Bn)>=liminfAn * liminfBn

i got the opposite resolt

where is my mistake:

http://img187.imageshack.us/img187/6705/44112683ho1.gif - Jan 9th 2009, 05:12 AMOpalg
Here's an example where the inequality is strict. You can test your argument against this example, to pinpoint where you went wrong.

Let $\displaystyle a_n = 2+(-1)^n$, $\displaystyle b_n = 2-(-1)^n$. Thus a_n is alternately 1 and 3, b_n is alternately 3 and 1. The lim inf for both sequences is 1. But when you multiply the sequences together you get a sequence where each term is 3. So the lim inf of the product is 3.

So $\displaystyle \liminf_{n\to\infty}a_nb_n = 3 > 1 = \liminf_{n\to\infty}a_n\liminf_{n\to\infty}b_n$. - Jan 9th 2009, 05:50 AMtransgalactic
i cant see the mistake

i am done this proof strictly on this definition

http://img515.imageshack.us/img515/5666/47016823jz1.gif - Jan 9th 2009, 10:29 AMOpalg
- Jan 9th 2009, 11:13 AMtransgalactic
why its not true??

in each of the following sequence our temporary inf

gets bigger or stays the same

so the function of the inf's goes up

and their limit is the least upper bound(b)

and the least upper bound is bigger or equal than every member

in the sequence.

can you tell me whats wrong with what i said? - Jan 9th 2009, 11:43 AMOpalg
- Jan 9th 2009, 12:22 PMtransgalactic
ok the limit is bigger or equal then any temporary inf of this sequence.

so what could i say the relations of the lim inf with the members of the sequence.

here i was given a solution

http://www.mathhelpforum.com/math-he...-question.html

and i was told that liminf is smaller than any temporary inf.

how he came to this conclusion?? - Jan 9th 2009, 12:24 PMtransgalactic
what is the relations of liminf with the members of a sequence

??