What does a universal initial mass function 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 lognormal 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