What does a universal IMF imply about star formation?
  We show that the same initial mass function (IMF) can result from very
different modes of star formation from very similar underlying core and/or
system mass functions. In particular, we show that the canonical IMF can be
recovered from very similar system mass functions, but with very different mass
ratio distributions within those systems. This is a consequence of the
basically log-normal shapes of all of the distributions. We also show that the
relationships between the shapes of the core, system, and stellar mass
functions may not be trivial. Therefore, different star formation in different
regions could still result in the same IMF.
