  Homogenization appeared more than 100 years ago. It is an approach to study
the macro-behavior of a medium by its micro-properties. In mathematics,
homogenization theory considers the limitations of the sequences of the
problems and its solutions when a parameter tends to zero. This parameter is
regarded as the ratio of the characteristic size in the micro scale to that in
the macro scale. So what is considered is a sequence of problems in a fixed
domain while the characteristic size in micro scale tends to zero. But for the
real situations in physics or engineering, the micro scale of a medium is fixed
and can not be changed. In the process of homogenization, it is the size in
macro scale which becomes larger and larger and tends to infinity. We observe
that the homogenization in physics is not equivalent to the homogenization in
mathematics up to some simple rescaling. With some direct error estimates, we
explain in what means we can accept the homogenized problem as the limitation
of the original real physical problems. As a byproduct, we present some results
on the mathematical homogenization of some problems with source term being only
weakly compacted in $H^{-1}$, while in standard homogenization theory, the
source term is assumed to be at least compacted in $H^{-1}$. A real example is
also given to show the validation of our observation and results.
