Date: Mar 21, 2013 6:26 AM
Subject: Re: Matheology § 224

On 21 Mrz., 09:14, Virgil <> wrote:
> While induction can certainly prove that no finite set of lines is
> sufficient, it cannot prove that an infinite set of lines cannot be
> sufficient,

It can prove that no finite line and no set of finite lines is
sufficient. Induction holds for every line of the list.

> because some infinite sets of lines clearly ARE sufficient,
> the set of all lines, for example, is both infinite and sufficient.

Ah so, "they clearly are".
Contemplate this parallel claim:
An infinite set of natural numbers clearly contains an infinite
number. Therefore infinite set of natural numbers clearly are
containing infinite numbers.

Regards, WM