> > As i understand it the numberline can never be a continuum unless you > set a limit or range, and they will be finite.
What a continuum _is_ you can learn from a topology text. Therein you will find a proof that the numberline is a continuum. It may not be called 'the numberline' (which rather prejudges the matter), it may be called blackboard bold R, or similar.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting