Date: Oct 5, 2017 12:15 PM
Author: Jim Burns
Subject: Re: It is a very bad idea and nothing less than stupid to define 1/3<br> = 0.333...

On 10/5/2017 9:59 AM, bursejan@gmail.com wrote:

> Doesn't make any sense, since it is a sequence
> and not a number. But obviously the decimal
> notation 0.999... refers to a number. So its
> simply lim n->oo (1-(1/10)^n), from the
>
> mathematical notational convention, that the
> ... in the above context includes the limit.


I am not familiar with a convention that includes the
limit as part of the sequence. That sounds like a bad idea
to me, not least because we can't assume that a particular
sequence has a limit.

In this discussion, no matter what you may be familiar with,
it's important to keep clear which we're talking about at
any point: the sequence or the limit of the sequence.

Anyway, what netzwelter wrote out is what I asked for,
that sequence defined without '...' My hope is that he
does not take your advice.

> Am Donnerstag, 5. Oktober 2017 15:50:38 UTC+2
> schrieb netzweltler:

>>> I mean a '...' at the end of the description.
>>> When one writes
>>> 0.9, 0.99, 0.999, ...
>>> one puts '...' at the end of _that_ but what does it mean?

>>
>> (1-(1/10)^n)n?N