Theory based on divisions of a whole?

[Riothamus]

I had a brief conversation regarding Set Theory being the fundamental math underlying all others.

I found myself wondering, if Set Theory is the grouping of separate objects, is there a theory regarding divisions of a whole, instead?

I am inclined to think such a theory, even if developed or possible, wouldn't be very useful for day to day applications, but once the scale of calculation gets large enough, like all the space or the relation among solar systems or galaxies, it might prove more elegant.

I also wonder at the implications for the types and values of numbers you would get.

So, does such a theory exist? If not, is it feasible?

 

[mathman]

I suggest you give some detail about what you mean. Set theory does cover questions about subsets, etc.