Given a multiset, e. g. S = {1, 1, 2, 3, 4, 4, 5}, what would be a short, concise notation to express the number of unique items in the multiset? (five in the given example).
2026-03-25 09:24:10.1774430650
Multiset: notation for size and number of unique items
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The set of unique items in multiset $S$ is usually called the support of $S$, and denoted $\operatorname{supp}S$. So, you can combine this with your preferred notation for number of elements: $\#$ or $|\cdot|$ to form $$\# (\operatorname{supp}S) \qquad \text{or}\qquad |\operatorname{supp}S|$$ Both are reasonably concise and are pretty descriptive.
According to OEIS Wiki, the cardinality of support of a multiset is called its dimension. Following this terminology, one could use $\dim S$. However, I don't find this as intuitive as either of the above options. And the usage of the term dimension may be somewhat narrow.