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I express variables $x_1, x_2, \ldots$ as "$x_i$'s".

Similarly, when I want to express sets $\mathcal{S}_1, \mathcal{S},2, \ldots$, I also use $\mathcal{S}_i$'s.

However, when I want to express the cardinalities of the sets, how to use??

  1. $\lvert\mathcal{S}_i\rvert$s ?
  2. $\lvert\mathcal{S}_i\rvert$'s ?

I thought at first to post this question on English question board, but because I want to hear the answer from mathematicians, I post here. If the topic is not right, let me know. I will delete it immediately.

Danny_Kim
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  • Simply write the cardinalities of the sets $S_i$. In this digital world it is advisable to trade brevity for clarity. – Fan Zheng Jul 05 '18 at 04:49
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    I’ve usually seen no use of “ ‘s “ in any of the above situations, but instead sentences like “the $x_i$ are linearly independent over $R$”, or, “ all the $\mathcal{S}_i$ are subsets of $\mathcal{S}$.” So I’d just say “the cardinalities of the $\mathcal{S}_i$.” – Nicholas Camacho Jul 05 '18 at 04:51
  • @NicholasCamacho is the statement "$f$ is computed by the blah-blah algorithm with given $N_j$'s" also weird? – Danny_Kim Jul 05 '18 at 05:23
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    I’m not sure, but I’d generally just stay away from “ ‘s “. The context usually lets the reader know that there are multiple $N_j$ in consideration. Technically, I don’t know if saying “$N_j$’s “ is wrong. So you could say “ f is computed by the algorithm with given $N_j$” is fine if it’s clear from context that there are many. Or just say “...with a given collection of $N_j$“ to emphasize that there are many. – Nicholas Camacho Jul 05 '18 at 18:13

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