TeXipedia

sim

Denotes mathematical similarity or approximate equality between expressions, commonly used in statistics and probability.

Overview

Essential in mathematical notation to indicate that values or distributions are similar or follow a particular distribution pattern.

  • Widely used in statistics to indicate random variables are distributed according to a specific probability distribution
  • Common in set theory and algebra to show similarity relationships
  • Appears frequently in academic papers and mathematical proofs when discussing approximations or distributional relationships
  • Often employed in machine learning and data science notation to describe probabilistic models

Examples

Expressing a random variable's distribution

X∼N(μ,σ2)X \sim N(\mu, \sigma^2) 
X \sim N(\mu, \sigma^2)

Indicating approximate equality or proportionality

f(x)∼x2 as x→∞f(x) \sim x^2 \text{ as } x \to \infty 
f(x) \sim x^2 \text{ as } x \to \infty

Denoting similarity between geometric shapes

△ABC∼△DEF\triangle ABC \sim \triangle DEF 
\triangle ABC \sim \triangle DEF