Evan Prodromou
#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 Prodromou
@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)
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).
Evan Prodromou
@briansullivan what I'm looking for is:
for all x memberof S, x < sum(S - {x})
Evan Prodromou
@kubefred So, that's not what Wikipedia says. Entirely possible that Wikipedia is wrong or unnecessarily complicated.
Max Effort
@evan I'm studying math for the fun of it, and just popped this question into an AI ... with that being said, it came back with:
The Subadditive Property : For a set S with elements {a1, a2, ..., an}, if no element is larger than all the other elements combined, then we can write this property as:
ai ≤ ∑_{j ≠ i} aj
This means that each element ai in the set is smaller or equal to the sum of all other elements.
The name for this specific mathematical concept is called Subadditivity ...
(Language model used was llama3.1)
Evan Prodromou
@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. "
Brian Sullivan
@evan It's not like ChatGPT is guaranteed to be correct. I fed it the exact question you asked in your post.
Evan Prodromou
@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
Sergio
@evan cryptocurrency bros might also have a name for it (because of the 51% attack thing)
Evan Prodromou
@galactus I think it would mess up real-world structures like federalism, too.
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