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eqsim

Denotes geometric or asymptotic equivalence between mathematical expressions, combining the concepts of equality and similarity.

Overview

Commonly employed in mathematical analysis and geometry to indicate that two expressions or objects are both equal and similar in nature.

  • Frequently used in asymptotic analysis to show that functions behave similarly as they approach a limit
  • Appears in geometric proofs when shapes or figures share both size and form properties
  • Useful in theoretical mathematics for describing relationships that are stronger than similarity but maintain geometric properties

Examples

Showing that two functions are asymptotically equivalent as x approaches infinity.

f(x)≂g(x) as x→∞f(x) \eqsim g(x) \text{ as } x \to \infty 
f(x) \eqsim g(x) \text{ as } x \to \infty

Indicating approximate equivalence between two expressions in statistical analysis.

θ^n≂N(μ,σ2)\hat{\theta}_n \eqsim N(\mu, \sigma^2) 
\hat{\theta}_n \eqsim N(\mu, \sigma^2)

Demonstrating asymptotic behavior in a series expansion.

∑k=1n1k≂ln⁡(n)+γ\sum_{k=1}^n \frac{1}{k} \eqsim \ln(n) + \gamma 
\sum_{k=1}^n \frac{1}{k} \eqsim \ln(n) + \gamma