Folkman’s theorem

Definition. (suggested new terminology) A set of natural numbers is said to be of critical mass fif there exist arbitrarily-large sets of natural numbers, all of whose sums belong to it.

Theorem. (Folkman’s theorem) Every finite partition of the set of natural numbers contains a member of critical mass.

Here is the link to the Wikipedia article on Folkman’s theorem.

keywords:
[Mathematics]
[Number Theory]
[Ramsey Theory]
[partitions]
[strength]
[size]
[summation]