In a posting to MathStackExchange, what I've labeld as the finite partitioning principle was answered to be implied by the principle that for every infinite set $X$, $X+X=X$, what I'd label as the Infinite Dedekindian Addition principle.
To quote the first principle:
By the finite partitioning principle I mean the following: Every infinite set is the union of pairwise disjoint finite sets all larger than 1 in cardinality. In other words every infinite set can be partitioned into a family of non-singleton finite compartments. Formally: $$\forall \operatorname {infinite} X , \exists Y: \\\forall a,b \in Y (a \cap b =\emptyset \land 1 < |a| < \aleph_0) \land X=\bigcup Y$$
What I want to ask here is:
What is the actual comparison between those two principles, is the finite partitioning principle strictly weaker than the Infinite Dedekindian addition principle? Or they are equivalent?
