Talk:Submodular set function

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Why would a submodular function be necessarily a subadditive function? I believe it requires nonnegativity. Peleg (talk) 15:16, 17 December 2011 (UTC)

Agreed. Somehow this point skipped my mind, since most submodular functions considered are nonnegative. But I have edited it to reflect this. Anonash (talk) 05:54, 10 February 2012 (UTC)

Introduction is difficult to comprehend

Introductory lines of the topic, or the topic definition is very difficult to comprehend. It must be splitted into short sentences. Especially this part is quite confusing: "that the difference in the value of the function that a single element makes "

Difference between current value of the function and previous value after adding new item????? — Preceding unsigned comment added by Osmankhalid2005 (talk • contribs) 18:23, 11 March 2013 (UTC)

Is the summary correct? =

"has the property that the difference in the incremental value of the function that a single element makes when added to an input set *decreases* as the size of the input set increases." I am not expert, but should not this be:

"has the property that the difference in the incremental value of the function that a single element makes when added to an input set *does not increase* as the size of the input set increases." — Preceding unsigned comment added by 84.182.57.56 (talk) 16:40, 17 March 2019 (UTC)

Formally yes, but such a wording sounds more ambiguous to me, as it could also be interpreted as "does not always increase", while the current wording is good enough for the lead. Tokenzero (talk) 20:31, 17 March 2019 (UTC)

Note that it says decrease, and not strictly decrease. I see though how the sentence can be confusing. How about this replacement: "In mathematics, a submodular set function (also known as a submodular function) is a set function who, informally, has the following property: the incremental value of adding a single element to the input decreases as the size of the input set increases." --Hous21 (talk) 20:37, 17 March 2019 (UTC)