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sqcap

Represents a square cap operator used in mathematical set theory and lattice operations.

Overview

Commonly employed in abstract algebra and mathematical logic to denote the meet operation in lattice theory or the intersection of sets with specific geometric interpretations.

  • Essential in lattice theory for representing the greatest lower bound (infimum) operation
  • Used in formal logic and set-theoretic proofs
  • Appears in advanced mathematics texts discussing ordered algebraic structures
  • Often paired with its dual operator square cup (\sqcup) in mathematical expressions

Examples

Representing the meet operation in lattice theory.

A⊓B={x∈X:x∈A and x∈B}A \sqcap B = \{x \in X : x \in A \text{ and } x \in B\} 
A \sqcap B = \{x \in X : x \in A \text{ and } x \in B\}

Showing the intersection of two finite dimensional vector spaces.

V1⊓V2=span{v1,v2}V_1 \sqcap V_2 = \text{span}\{v_1, v_2\} 
V_1 \sqcap V_2 = \text{span}\{v_1, v_2\}

Expressing the greatest lower bound in a semilattice.

x⊓y⊓z=(x⊓y)⊓zx \sqcap y \sqcap z = (x \sqcap y) \sqcap z 
x \sqcap y \sqcap z = (x \sqcap y) \sqcap z