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## a possible quasimetric on a space formed by words [closed]

Hi all. Today in my research I found a conjecture.

Let $S$ be the set of all words of a language. Define the function $N: S\times S \rightarrow R_+$ such that $N(x, y) =$ number of journal articles about $x$ that the word $y$ appears. Obviously: $N(x, x) \ge N(x, y)$ for all $x, y \in S$ and it can be assumed that the $N(x,x) = N(x,y)$ only for $x=y$.

Define $dep(x, y) = N(x, x) - N(x,y)$. Is $dep$ a quasimetric?

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ashade, it is likely that this question will be closed soon since this function $N$ is not at all well-defined. It is rather subjective to decide what it means for an article to be "about $x$". – Vidit Nanda Aug 21 at 2:18
Vel, I'm sorry for that. However, I thought people could answer in the form "assuming N is like... then". Also, I thought this forum was for researchers to help each other, and not a battle for the coolest question / answer. There are 10 hours I post the question and it is already closed! I had no time to edit it, no second chance, since I was sleeping when the question was closed. My sugestion: let's give the author of the question a warning and a full day for him to edit it. If it isnot changed, then close it. – ashade Aug 21 at 12:28
Maybe the answer, ashade, is to formulate the question well before you post it. – Bill Johnson Aug 23 at 4:44