Hi I was wondering how I could prove the following:

If a functionfis defined on an unbounded above domainandis eventually monotone and eventually bounded,

then

Any help? Thanks

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- Oct 15th 2009, 05:04 PMdannyboycurtislimit at infinity proof
Hi I was wondering how I could prove the following:

If a function*f*is defined on an unbounded above domain*and*is eventually monotone and eventually bounded,

then

Any help? Thanks - Oct 15th 2009, 07:41 PMrn443
- Oct 15th 2009, 08:38 PMtonio

This is, imo, an odd-worded question: is D, the domain, unbounded above, but then f is "eventually" (what does this mean mathematicalwise?) monotone and bounded? Well, if it has some more or less intuitive meaning, then f is bounded so how can it go to oo??

Try to word out the problem more clearly, perhaps that'll help to undestand what's going in here.

Tonio - Oct 16th 2009, 12:06 PMdannyboycurtis
Hi I was wondering how I could prove the following:

If a function*f*is defined on a domain http://www.mathhelpforum.com/math-he...dbead2c9-1.gif [WHERE D IS UNBOUNDED ABOVE]*and*is eventually monotone and eventually bounded,

then http://www.mathhelpforum.com/math-he...43e6ec87-1.gif

Any help? Thanks - Oct 16th 2009, 01:56 PMtonio
- Oct 17th 2009, 07:24 PMbinkypoo
If f is defined on a set then f is

__eventually bounded__on D if such that ,

If f is defined on a set then f is__eventually monotone__on D if and , either or

I believe if one looks at the function as a sequence the word 'eventually' is definitely defined in mathematics, as in 'eventually' monotone sequences where

for some but where for some smaller n and m. - Oct 17th 2009, 08:31 PMredsoxfan325
Well, those are the definitions of

*bounded*and*monotone*. The questions everyone's been asking are:

1) What is this "eventually" business?

2) How can anything bounded ever have a limit approaching infinity?

Until some things are cleared up, no one is going to be able to help. - Oct 17th 2009, 08:50 PMbinkypoo
It seems that a sequence a_n can be monotone for n>N but for n<N it may not be. Hence this sequence would be eventually monotone rather than strictly monotone.

like this sequence:

4,3,2,1,2,3,4,5,6,7,8,9,.... - Oct 18th 2009, 04:40 AMHallsofIvy
And we could say that a function, f, is "eventually bounded" if and only if there exist and M such that if , then |f(x)|< M.

But we still have the problem that if f is "bounded"**or**"eventually bounded", its limit**cannot**be .