Thread: SETS - (k+1)-element subset S

There is a natural number . Prove that from any set consisting of integer numbers that has more than elements we can take a subset S that has elements and:
For any two different subsets the sum of all elements of set is different from the sum of all elements of set . (We assume that the sum of all elements of an empty set equals 0).

I would be really grateful if anyone could help me with this assignment.

Maybe we can try to prove it inductively...

But I don't know how do get down to it anyway.