It seems clear there is a place in physics
for the mathematics of infinity, and in fact
and indeed much of extra-classical mathematical
physics sees the symmetries or reflection of
the classical in the meso-scale about the infinite
in extent and infinitesimal in exent, the total
and point for the global and local.
Key to this then is the extent of the support of
mathematical foundations for foundations of the
mathematical physics.
Where the features of the physics plainly enough
_are_ the features of the mathematics, then finding
new features of common structures in the mathematics
automatically so equips the physics with these features.
Here these "new features" are of the points in the line
themselves, that there are models of R the real numbers
of line continuity (as above), field continuity (as usual),
and signal continuity (as consequent) that would find
relevant placement variously in the models of the
physical regimes.
Here this isn't so much about the various models in physics
themselves of the fluid model or the wave model and how
these today may commonly yet be but a partial perspective
of the true nature of things, it is already a richer
substrate of the elements of the continuum themselves
that advises what occurs of these effects of the "particle"
in the configuration (or as Bohr puts it, arrangement) and
energy of experiment that so yields the _effects_ in physics,
as they are direct effects, as it were, in mathematics.
So, yeah, the points in a line
from zero to one are a continuum.
Also they're uniform and regular there,
constant monotone increasing as it were.