Formula for (word) frequency count

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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?