The rational number line has a finite beginning in history. You may study its origins.
The concept emerged in various lineages, threads, partially overlapping, and continuing through our own day (though some have fizzled, others started up).
You can do some kinds of mathematics without any infinite lines of any kind, and still be considered rational. Depends on your school and its authorities.
If you're in a school that browbeats you into thinking there's only "one right math" (or way of teaching it), you might want to shop around.
Some maths just have "types" such as integer, float, double, complex, extended, decimal etc. Rational number may be among them, or not (Python's has it).
No lines may be included in some of these languages (grammars), but you don't necessarily need them for implementation purposes.
If you forget what a "number line" is, don't think you've forgotten the core of math. Many maths would live without today's "number line" just fine. Others wouldn't.
On Sun, Nov 25, 2012 at 5:23 PM, Jonathan Crabtree <firstname.lastname@example.org> wrote:
> What is the best answer to the simple question:
> "Where does the rational number line start?"
> Yes it goes on forever in both directions and we can all agree on that. Yet does that mean a line that goes forever in two directions does not have any starting point?
> For on-topic discussion purposes, I'm talking about a single rational number line and not about the real continuous line or complex number plane.
> So where does the rational number line start?
> Or do we tell a child it doesn't start anywhere because it doesn't end anywhere?