# Does this mathematical result have a specific name?

I am not sure if it's new although it may be an easy consequence of some theorem or lemma.The result is as follows: By choosing a set of numbers between $$0$$ and $$n$$(for any $$n$$) picking each number at most once and summing them you can create any number between 0 and $$n(n+1) / 2$$ . The above result can be easily proven by induction.

• This is a roundabout way of defining triangular numbers. $T_n = 1+2+3+...+n = n(n+1)/2$ which is typically proved inductively. Add up a subset of $\lbrace 1...n\rbrace$, you get a smaller number. Nov 16 '20 at 23:17
• I do not think there is a special name for this but it is a special case of the subset sum problem: the subset sum set of an initial segment of natural numbers is another initial segment of natural numbers. Nov 17 '20 at 8:58