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 > 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.