notes_on_mc

We start with some smf a at z0
We end with another smf b at z1

In the process of getting from a - b there are some mergers.

### One
This means that in b there are some galaxies that are made up of two galaxies
We want to break each of those galaxies back into their component parts.

for various final masses (m at b)
  They have number density y
  for various mass ratios ranges (u)
    find the number of mergers with ratio within u galaxies of mass m have undergone between a and b (mu)
    add y * mu to galaxies of the correct masses. subtract y * mu to glaxies of m

### Other way
This means that in a there are some galaxies that do not exist in b
Every time there is a merger resulting in a galaxy of mass m at ratio r, a galaxy of mass m/(r+1) vanishes and a galaxy of (mr/(r+1)) too

For various start masses (m at a)
  They have number density y
  Assume this is the smaller partner
  for various mass ratio