Re: Terminology problem

From: Edo (eddod_at_eddododod.dod)
Date: 11/10/04 

Date: Wed, 10 Nov 2004 06:32:37 -0800

Randy Poe wrote:

> Edo wrote:
>
>>Hello
>>
>>I am scratching my head on this, don't understand what it means.
>>
>>it is a sequence theorem
>>Given the sequence {a_n} if have a function f(x) such that f(n)=a_n
>
>
> OK, so we start with a sequence of values {a_n}. We define
> a function f(x) which takes on those values whenever x is
> a natural number. In other words, we plot a sequence of
> points (n, a_n). We plot our sequence {a_n} as point on
> an x-y graph.
>
> Now we're going to define a function which goes through
> those points, connecting the dots. We haven't said anything
> yet about what happens to that function between the dots,
> and we don't know anything about this sequence yet.
>
>
>>and lim(x->Inf) f(x)=L
>
>
> Now we know something more about our connect-the-dots
> function, namely that it converges to a limit as x->Inf.
> Since f(x) is defined at all x>0, this means we also
> get converging sequences of values when we take x at
> in-between values.
>
>
>>then lim(x->Inf) a_n =L
>
>
> I assume that this limit was for n->inf, not x->inf.
>
>
>>it seams like there may be an implied connection between f(x) and
>
> f(n)
>
>>that I just don't know.
>
>
> It's making a connection between two different types
> of convergence. The connection between f(x) and f(n)
> is made by assumption at the start: f(x) takes on the
> values a_n at x=n.
>
> Review the definitions of those two types of convergence
> (function and sequence).
>
> - Randy
>

thanks, I understand now.

Sure google puts out some, but can you recommend a good online ref.
“links” to function and sequence.

thanks

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