You're taking an anomalously narrow view of the parent comment. Say the minimum distance is one inch.

You want to say that the concept of half an inch lacks physical representation, but that isn't true. You can easily demonstrate it as the ratio between one inch and two feet, compared to the reference ratio between one inch and one foot.

dhosek is saying that in a quantized space, there are reals that cannot be demonstrated this way, and he is right, but the same thing is untrue of rationals.

("In a quantized space", by the way, just means that all measured quantities are necessarily integers. That causes all kinds of problems, but "lacking examples of arbitrary rational numbers" isn't one of them.)

> You can easily demonstrate it [half an inch] as the ratio between one inch and two feet, compared to the reference ratio between one inch and one foot.

You seem to have your units confused. Half an inch is a distance, while ratios, or comparisons of ratios, are all dimensionless scalars.