In the context of chopping a line into pieces, potential infinity would mean that the line could be cut into more and more pieces, as many as desired but still always a finite number and all of nonzero length. That’s perfectly permissible and leads to no logical difficulties. What’s verboten is to imagine going all the way to a completed infinity of pieces of zero length. That, Aristotle felt, would lead to nonsense — as it does here, in revealing that zero times infinity can give any answer. And so he forbade the use of completed infinity in mathematics and philosophy. His edict was upheld by
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