I have a homework assignment where, given some definitions, I need to prove that every set has a partition. There were some very elaborate ideas on how to prove this, but I realized that the definitions we were given allow a set to be a partition of itself. And if that is the case, then there clearly exists a partition of every set.
I'm not sure if I'm taking advantage of the simplicity of the definitions we are given. I tried to search if a set is a partition of itself, and not much if anything came up. The claim "every set is a partition of itself" seems to violate our english definition of partition, but be consistent with the mathematical definitions I have found.
For the sake of this discussion, I would think it be best to only consider non-empty sets because there seems to be some variety in how partitions are defined that prohibit the empty set from having partitions.