Full Idea
In defining continuity one is almost bound to rely on the notion of infinity; it is because the continuous is what is infinitely divisible.
Gist of Idea
Continuity depends on infinity, because the continuous is infinitely divisible
Source
Aristotle (Physics [c.337 BCE], 200b18)
Book Reference
Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.56
A Reaction
Parmenides and the Achilles Paradox lie behind this view, and the fact that Aristotle was opposed to the view that some things are indivisible ('atomism'). Nice point, though - that space and time immediately imply the infinite.