preccurlyeq
Denotes a curly less than or equal to relationship, commonly used in mathematical order theory and set comparisons.
Overview
Serves as a specialized mathematical operator indicating a preorder or precedence relationship with a distinctive curly style, enhancing visual clarity in complex mathematical expressions.
- Frequently used in abstract algebra and order theory to denote partial orders
- Common in formal mathematical proofs where precise ordering relationships need to be distinguished
- Particularly useful in lattice theory and set theory contexts where multiple ordering relations appear together
- Often appears alongside similar relations like \prec and \preceq to indicate subtle distinctions in ordering relationships
Examples
Expressing a preorder relation between elements in set theory.
A \preccurlyeq B \implies |A| \leq |B|Comparing partially ordered multisets.
\{1,2,2\} \preccurlyeq \{1,2,2,3\}Defining a refinement relation between partitions.
P_1 \preccurlyeq P_2 \iff \forall x \in P_1, \exists y \in P_2: x \subseteq y