Full Idea
It seems obvious that 'part' stands for a partial ordering, a reflexive ('everything is part of itself'), antisymmetic ('two things cannot be part of each other'), and transitive (a part of a part of a thing is part of that thing) relation.
Gist of Idea
'Part' stands for a reflexive, antisymmetric and transitive relation
Source
Achille Varzi (Mereology [2003], 2.1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.4
A Reaction
I'm never clear why the reflexive bit of the relation should be taken as 'obvious', since it seems to defy normal usage and common sense. It would be absurd to say 'I'll give you part of the cake' and hand you the whole of it. See Idea 10651.
Related Idea
Idea 10651 If 'part' is reflexive, then identity is a limit case of parthood [Varzi]