Re: abundance of irrationals!)

"Randy Poe" <poespam-trap@xxxxxxxxx> wrote in message news:<1113499436.071675.26170@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>...

> Proof that lim(n->oo)1/n = 0:
>
> Let eps be any positive value. Define n0 = ceiling(1/eps)
> so n0 >= 1/eps and 1/n0 <= eps.
>
> Then for all n>n0, 1/n < 1/n0 <= eps.
>
> Thus |1/n - 0| < eps for all n > n0, and I have established
> that lim(n->oo)1/n = 0.
>
> Note that the statement 1/n < 1/n0 refers to finite values
> of n. Note that the statement 1/n < 1/n0 is true for all
> finite values of n with the property that n>n0. Thus,
> as I said, I have considered only what happens with
> finite values of n, and by doing so I have proven
> the limit to be 0.
>
> As I said, this limit was evaluated by considering
> only properties of finite values of n.

Sequences cause no problems, because all n are finite. Series cause
problems, because N is said to be infinite. Please repeat your proof
for the infinite Sum 1/2^k = 1, and you will see where you fail.

Regards, WM
.

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