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ntriangleleft

Represents a negated left-pointing triangular relation symbol used in mathematical logic and set theory.

Overview

Serves as a specialized mathematical operator primarily employed in advanced mathematical notation where negated triangular relationships need to be expressed.

  • Common in formal logic and abstract algebra for denoting non-strict ordering relationships
  • Often used alongside its counterpart \ntriangleright in mathematical proofs and theoretical computer science
  • Particularly useful in contexts involving partial orders, lattice theory, and advanced set theoretical notation
  • Appears in academic papers and advanced mathematical texts where precise logical relationships must be denoted

Examples

Expressing that a sequence is not left-convergent.

{xn}⋪x\{x_n\} \ntriangleleft x 
\{x_n\} \ntriangleleft x

Denoting a non-dominated relation in order theory.

a⋪b  ⟹  a≰ba \ntriangleleft b \implies a \not\leq b 
a \ntriangleleft b \implies a \not\leq b

Representing non-refinement in formal specifications.

P⋪Qmeans P does not refine QP \ntriangleleft Q \quad \text{means } P \text{ does not refine } Q 
P \ntriangleleft Q \quad \text{means } P \text{ does not refine } Q