The Paradox of Plurality (Extension)

This is another of Zeno’s paradoxes, rather less easy to handle than the others.

Read Cantor’s Paradox first. Since we are considering dividing the segment not physically

but in thought, this is a paradox about the abstract geometrical line. Each halving of a part of a finite line determines a shorter interval, so that denumerably many halvings can determine a nest of intervals which have only one point in common.