  We provide a multiple integral representation for each multiple zeta-star
value, and utilize these representations to establish a natural order structure
on the set of such values. This order structure allows for a one-to-one
correspondence between a subset of the infinite sequences of natural numbers
and the half line $(1,+\infty)$. Some basic properties of this correspondence
are discussed. We also calculate the Hausdorff dimensions for the images of
some subsets of the infinite sequences under this correspondence. As a result
of this correspondence, we are able to determine the limits for a number of
natural multiple integrals. Our analysis also reveals that the set of multiple
zeta-star values is dense within the $(1,+\infty)$ domain, and that each value
is non-integer in nature.
