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#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.

Brian Sullivan

@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)

en.wikipedia.org/wiki/Subaddit

@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. "