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I searched for a mathematical formula for the description of (word) frequency count. Its definition would be:

A word frequency count is a measure of the number of times that a word w occurs in some corpus n.

I was thinking about something like this maybe?

$freq_{word} (w) = \sum w \in n$

What I would mean by this formula is:

the word frequency of w = the sum of (every occurrence of) w being a member of n

I have absolutely no strong mathematical background, but I just started experimenting with using actual formulas as a theoretical support for methodologies (in linguistics). Is this formula worth anything or is it absolute nonsense and am I using it incorrectly?

  • As you want to count the number of times that a word $w$ occurs in $n$, it is natural to create a function that gives you $k$ if $w$ occurs $k$ times in $n$. Of course you have to feed your function the two arguments $w$ and $n$. So it should look like: $$f:\Omega \times \Omega \rightarrow \mathbb{N}\ f(n,w):=k,\ \text{whenever $w$ occurs in $n$ $k$ times}$$ – b00n heT May 13 '16 at 12:55
  • And what does $\Omega \times \Omega$ denote here? –  May 13 '16 at 13:00
  • $\Omega$ is just the set of all phrases. (This formula is just a little bit more general, as it allows you to count the number of subphrases and not just words). Of course you should also define what "occurrence" here means, to avoid overcounting, but it is quite obvious. – b00n heT May 13 '16 at 13:02
  • @b00nheT: I don't think that is neither "natural" nor does it answer the question. – miracle173 May 13 '16 at 14:26
  • I admit that mine is not the answer to the OP's question, but I was to lazy to analyze every error... About the naturality, I most definitely counter your opinion and ask that you provide an answer which you find more "natural". – b00n heT May 13 '16 at 15:02
  • @b00nheT I hoped for a more elegant, less hard core mathematical formula, as that would be less suited for its purpose (linguistics paper). But thanks anyway - I now have learned more about building mathematical functions! ;) –  May 15 '16 at 01:09

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