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curlyeqsucc

Denotes a curly equals followed by succeeds relation in mathematical expressions, combining equality and succession into a single symbol.

Overview

Serves as a specialized mathematical relation symbol that combines the concepts of equality and succession, primarily used in advanced mathematical notation and formal proofs.

  • Common in abstract algebra and set theory for describing specific relationships between elements or sets.
  • Useful when expressing ordered relationships that also maintain some form of equivalence.
  • Often appears alongside similar relation symbols in formal mathematical writing where precise relationship notation is crucial.

Examples

Showing a sequence relationship where each term succeeds and is equivalent to the previous.

xn⋟xn+1⋟xn+2x_n \curlyeqsucc x_{n+1} \curlyeqsucc x_{n+2} 
x_n \curlyeqsucc x_{n+1} \curlyeqsucc x_{n+2}

Demonstrating ordered equivalence in a mathematical sequence.

a1⋟a2⋟a3⋟a4a_1 \curlyeqsucc a_2 \curlyeqsucc a_3 \curlyeqsucc a_4 
a_1 \curlyeqsucc a_2 \curlyeqsucc a_3 \curlyeqsucc a_4

Expressing successive equivalent transformations in an equation.

f(x)⋟g(x)⋟h(x)f(x) \curlyeqsucc g(x) \curlyeqsucc h(x) 
f(x) \curlyeqsucc g(x) \curlyeqsucc h(x)