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backsimeq

Denotes a backwards similar-or-equal relationship between mathematical expressions, combining reverse similarity with equality.

Overview

Serves as a specialized mathematical relation symbol primarily used in advanced algebra and theoretical mathematics where backwards similarity with equality needs to be expressed.

  • Common in abstract algebra and mathematical logic for describing specific relationships between elements or sets
  • Often appears in proofs and formal mathematical writing where precise relationship notation is crucial
  • Provides a variant to the standard similar-or-equal symbol when the reverse relationship needs to be emphasized

Examples

Expressing an asymptotic equivalence relationship between functions.

f(x)⋍g(x) as x→∞f(x) \backsimeq g(x) \text{ as } x \to \infty 
f(x) \backsimeq g(x) \text{ as } x \to \infty

Showing approximate backward similarity in a mathematical expression.

x2+1⋍x for large x\sqrt{x^2 + 1} \backsimeq x \text{ for large } x 
\sqrt{x^2 + 1} \backsimeq x \text{ for large } x

Indicating reverse asymptotic behavior in limit notation.

lim⁡n→∞n+1n⋍1\lim_{n \to \infty} \frac{n+1}{n} \backsimeq 1 
\lim_{n \to \infty} \frac{n+1}{n} \backsimeq 1