# Mathematical notation for expressing the top n elements

I would like to know what is the mathematical notation to express the top n elements. Look at the equation below. Here $x_w$ is a feature vector representing the contribution of a particular word $w$. $N_w$ is the count or frequency of the words. In the following equation, I am assigning 0 weights to (1). the top 50 words and (2). words with frequency < 10. I would like to know how to express the top 50 words using a better mathematical notation
$x_{w} = \begin{cases} 0 & \text{ if } N_w\in \text{top$50$elements} \\ 0 & \text{ if } N_w < 10 \\ N_w & \text{ otherwise } \end{cases}$

• Top fifty elements among which other elements? I don't get it. Jun 16, 2014 at 17:05
• The top 50 highest frequency words.
– tan
Jun 16, 2014 at 17:51

Instead of $N_w$, call the number of instances of the word $w$ by $N(w)$. Subscript the words numerically according to the rule $i < j$ if $N(w_i)$ > $N(w_j)$.
We have now fully ordered the set of (different) words. Let T = {$w_i$ | $i$ < 51 or if $N(w_i) < 10$}. You can now replace your top50elements with T and collapse the first two categories into one.