TeXipedia

nparallel

Denotes non-parallel relationship between geometric objects or mathematical expressions in advanced mathematics.

Overview

Serves as a negation of the parallel symbol, commonly used in geometry, linear algebra, and advanced mathematical proofs to indicate that two or more objects (like lines, planes, or vectors) are not parallel to each other.

  • Essential in geometric theorems and proofs where non-parallel relationships need to be explicitly stated
  • Appears frequently in advanced algebra and topology discussions
  • Used in mathematical logic and set theory to express contradictions to parallel properties
  • Particularly useful in educational contexts when teaching geometric concepts and relationships

Examples

Stating that two lines are not parallel in a geometric proof.

If L1∦L2, then the lines must intersect at some point.\text{If } L_1 \nparallel L_2 \text{, then the lines must intersect at some point.} 
\text{If } L_1 \nparallel L_2 \text{, then the lines must intersect at some point.}

Expressing that two vectors are not parallel in linear algebra.

u⃗∦v⃗  ⟹  ∃k∈R:u⃗≠kv⃗\vec{u} \nparallel \vec{v} \implies \exists k \in \mathbb{R} : \vec{u} \neq k\vec{v} 
\vec{u} \nparallel \vec{v} \implies \exists k \in \mathbb{R} : \vec{u} \neq k\vec{v}

Describing non-parallel planes in 3D geometry.

P1∦P2  ⟹  the planes intersect in a lineP_1 \nparallel P_2 \implies \text{the planes intersect in a line} 
P_1 \nparallel P_2 \implies \text{the planes intersect in a line}