Notation for sets that do not overlap
Is there notation to describe, say a set that consists entirely of two mutually exclusive subsets?
Say $ D = D_1 \cup D_2 $, how to indicate that $D_1$ and $D_2$ do not overlap?
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$\begingroup$The intersection of the two subsets is the empty set if they don't overlap:
$$D_1 \cap D_2 = \emptyset$$
This statement can be used with (not in place of) the one in your question to describe what you want.
$\endgroup$ $\begingroup$$D_1 \sqcup D_2$ and $D_1 \stackrel{\circ}\cup D_2$ [possibly with the circle or dot lower within the 'cup'] are both used, to denote the union of $D_i$ when you want to emphasize that the $D_i$ are disjoint. Sometimes "disjoint union" is meant to be an operation in its own right, guaranteeing disjointness of the operands before forming their union. For example, $$ D_1 \sqcup D_2 := \{0\}\times D_1 \cup \{1\}\times D_2. $$ In either case, an author will (should) make clear what the symbol will denote.
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