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For a paper I have a set of particles which I usually reference by $ p $. The paper is physics related, so I haven't made any real formal definition of the set, and always just relate to them as "the particles". I use it as

$$ m_{i} = \sum\limits_p m_p w_{ip}. $$

Now I would like to introduce another set of particles $ q $ which is a subset of $ p $. How should I mathematically describe this simply? I want to write something like

$$ q \subset p, $$

however it's a little weird as $ q, p $ is not sets per say but just running indices. Do you have any suggestions?

Asaf Karagila
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pingul
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  • In fact I prefer this (and @SiddharthBatt 's answer) to indexing the elements with (artificial) integer subscripts.In mathematics it might be more customary to use upper case letters for sets. – Ethan Bolker May 27 '16 at 18:41
  • @EthanBolker That is also I reason I felt my expression felt weird and not really satisfying. I think I lacked the proper way of expressing the sets $ P $ and $ Q $, which was why I did not make the connection myself. – pingul May 27 '16 at 18:49

2 Answers2

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you can write

$$ \sum_{p \in P} <expr(p)> $$

where $P$ is the set of particles, and $p$ is the index that runs over $P$

and then later say that $Q \subset P$. To run indeces over $Q$, do the same thing and use something line

$$ \sum_{q \in Q} <expr(q)> $$

Siddharth Bhat
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Let $P$ be an index set for the set of particles. For instance $P = [1,K] \subset \Bbb{Z}$ where $K$ is the number of particles. Write your sum(s) as $\displaystyle \sum_{p \in P} \dots$. Then let $Q \subset P$.

Eric Towers
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