#Math friends: what is the name of the property of a set such that no member of the set is larger than all the other members combined?
{1, 3, 500} does not have this property; {3, 4, 5} does.
Assuming some way to compare members and some way to combine them.
@evan The property you're describing is called a subadditive property.
In a subadditive set, no individual element is greater than the sum (or combined size) of all the other elements in the set.
(ChatGPT’s answer anyway).
@briansullivan I'm not sure about that. Here's what Wikipedia says about a subadditive sequence (not set):
for all n, m: a(n+m) <= a(n) + a(m)
@briansullivan what I'm looking for is:
x memberof S -> x < sum(S - {x})
@evan It's not like ChatGPT is guaranteed to be correct. I fed it the exact question you asked in your post.
@briansullivan I know! Not holding you responsible. Here's the question I asked before posting:
Me: "Let's say we have a set of integers. What is the name for the property of such a set that says that no one member is bigger than the sum of the other members?"
ChatGPT: "The property you're describing is called the Helly property or Helly's condition for a set of integers. Specifically, this means that no element in the set is greater than or equal to the sum of the other elements in the set. "
@briansullivan This doesn't seem to be the definition of the Helly property at all, at least according to Wikipedia:
https://en.wikipedia.org/wiki/Helly_family#The_Helly_property