Proving BinPacking is NP-complete given Partition problem is NP-hard I'm trying to prove that the BinPacking problem is NP hard granted the partition problem is NP hard. If I have E a set of positive integers, can I split it into two subsets such that the sums of the integers in both subsets are equal?
The polynomial reduction I found would be the following:

*

*My objects O are defined as what's in E (the weight of each object is the integer value and |E| is the number of objects)

*Number of bags = 2

*Capacity of each bag is half of the sum of everything in E

Is this wrong because my polynomial reduction only reduces to BinPacking with 2 bags whose capacity are the same?
I’m skeptic because if I carry out this proof, and I find an algorithm in polynomial time for the partition problem I will only have proof that BinPacking with 2 bags whose capacity are the same is solvable in a polynomial time.

It is not wrong, you effectively reduce only some of the BinPacking problem instances.
You will only have an explicit solution for BinPacking with 2 bags, this is correct also.
