On 1 Feb, 15:10, Frederick Williams <freddywilli...@btinternet.com> wrote: > JT wrote: > > > 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.
There can not be any continuum without a range start and end point, a single natural ia a continuum it has a start and endpoint. The naturals are discrete and do not have a specific range so there is no continuum holding them until you can set a start and end point problem is you can never reach the endpoint and that is because the naturals works bottom up you will never find the end point there is always a next.
With fractions it is different there you work top down from the continuum (a single natural) and partition it there is no last row or item in the base branches from the fractional natural either but you have the start and end point.
> -- > 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