They may not know the term “metric space” (in which case you just explain that it’s a setting where we can measure distance), but if they think larger numbers are “closer to infinity” than smaller numbers, that means they are intuitively thinking in terms of the extended real line (metrized in one of the usual ways).
They may not know the term “metric space” (in which case you just explain that it’s a setting where we can measure distance), but if they think larger numbers are “closer to infinity” than smaller numbers, that means they are intuitively thinking in terms of the extended real line (metrized in one of the usual ways).