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circeq

Denotes a circular equality relationship between mathematical expressions, indicating equivalence under cyclic permutation.

Overview

Primarily used in abstract algebra and group theory to express cyclic relationships or rotational symmetries between mathematical objects.

  • Common in permutation group notation and cyclic group theory
  • Helpful when describing periodic or cyclical mathematical patterns
  • Often appears in advanced algebra texts and research papers discussing symmetry properties
  • Useful for expressing equivalence classes under cyclic transformations

Examples

Defining a circular equivalence relation between two sets.

AB    A=BA \circeq B \iff |A| = |B|
A \circeq B \iff |A| = |B|

Expressing circular congruence in modular arithmetic.

xy(modn)x \circeq y \pmod{n}
x \circeq y \pmod{n}

Denoting cyclic equivalence in group theory.

g1g2 in G/Hg_1 \circeq g_2 \text{ in } G/H
g_1 \circeq g_2 \text{ in } G/H