TeXipedia

nshortparallel

Represents a negated short parallel relationship between mathematical objects, indicating they are explicitly not parallel.

Overview

Serves as a specialized mathematical notation primarily used in geometry and linear algebra contexts where it's necessary to explicitly denote non-parallel relationships between lines, planes, or vectors.

  • Common in geometric proofs and mathematical demonstrations where parallel relationships need to be negated.
  • Provides a more compact alternative to the standard negated parallel symbol.
  • Particularly useful in tight spacing situations where the regular-length negated parallel symbol would be too large.
  • Often appears in academic papers and technical documents discussing geometric relationships.

Examples

Negating the short parallel relationship between two geometric objects.

A∦B  ⟹  A intersects BA \nshortparallel B \implies A \text{ intersects } B 
A \nshortparallel B \implies A \text{ intersects } B

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

l1∦l2  ⟹  ∃P(l1∩l2)l_1 \nshortparallel l_2 \implies \exists P(l_1 \cap l_2) 
l_1 \nshortparallel l_2 \implies \exists P(l_1 \cap l_2)

Showing non-parallel vectors in vector algebra.

u⃗∦v⃗  ⟹  u⃗⋅v⃗≠k∣u⃗∣∣v⃗∣\vec{u} \nshortparallel \vec{v} \implies \vec{u} \cdot \vec{v} \neq k|\vec{u}||\vec{v}| 
\vec{u} \nshortparallel \vec{v} \implies \vec{u} \cdot \vec{v} \neq k|\vec{u}||\vec{v}|