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]

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