Date: Mar 21, 2013 6:26 AM
Subject: Re: Matheology § 224
On 21 Mrz., 09:14, Virgil <vir...@ligriv.com> 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
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.