1 Jamie: The myth is that parallel lines meet at infinity. So we'll draw some parallel lines...
2 Jamie: ... and head out to the edge of this infinite featureless plane to see if they meet.
2 Death of Inhaling Hatmaking Chemicals: JUST A MO', GUV.
3 Death of Inhaling Hatmaking Chemicals: 'AFORE BUSTIN' ANY MYFFS, I 'AFF TO PROCESS YOUR DEFF BY INSANELY O'ERPOWERED FIREBALL.
4 Death of Insanely Overpowered Fireballs: {manifesting suddenly, with Adam} AHEM.

No, I don't know how they can travel to the edge of the Infinite Featureless Plane either*. I just thought it would be a funny thing to try to investigate experimentally.

* Actually, you could probably do it by mapping yourself on to a Riemannian manifold of some sort with an asymptotic metric or something. Assuming you can arbitrarily change your space-time metric, of course. Sorry, I'll stop now.

---

2018-04-08 Rerun commentary: On further thought, you might not need to travel all the way to the edge of the Infinite Featureless Plane to disprove the myth. If the parallel lines intersect before the edge, you'll notice it without having to reach the edge.

To prove the myth, on the other hand, you need to inspect everywhere and show that the lines don't meet anywhere.

Never mind the question of how you draw parallel lines that extend everywhere.