Date: Nov 16, 2012 11:53 AM
Subject: Re: Matheology § 152
"LudovicoVan" <ju...@diegidio.name> wrote:
> What is the limit of the sequence of the sets of indexes on the left
> hand side?
oo is not a natural number but indices are natural numbers because
they determine a position. oo is not a position.
> What is the limit of the decimal numbers?
By the same basic arithmetic: note that if you disallow the first,
should disallow the second on exactly the same grounds.
Talking about the limit oo does not mean that it is assumed. It means
that the sequence grows beyond every finite positive number.
Also the sequence (1/n) does never assume its limit 0. Only the
difference between 1/n and 0 shrinks below every positive number.