Page "Asymptote" Paragraph 8

The idea that a curve may come arbitrarily close to a line without actually becoming the same may seem counter to everyday experience.

The representations of a line and a curve as marks on a piece of paper or as pixels on a computer screen have a positive width.

So if they were to be extended far enough they would seem to merge, at least as far as the eye could discern.

But these are physical representations of the corresponding mathematical entities ; the line and the curve are idealized concepts whose width is 0 ( see Line ).

Therefore the understanding of the idea of an asymptote requires an effort of reason rather than experience.