---
title: "Tilde mathematical notation"
description: "A context-sensitive mark for probability distributions, asymptotic equivalence, equivalence relations, and approximate or perturbed objects."
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/tilde"
md_url: "https://fanout.sh/labs/math-decoder/symbol/tilde.md"
last_updated: "2026-08-09"
access: "public"
---

# Tilde mathematical notation

A context-sensitive mark for probability distributions, asymptotic equivalence, equivalence relations, and approximate or perturbed objects.

## Public overview

Distributed as: States that a random variable follows the probability distribution written on the right. Example: X follows a normal distribution with mean zero and variance one.

Asymptotic equivalence: States that the ratio of two functions approaches one in the specified limiting regime. Example: For large n, the ratio f of n over g of n approaches one.

Equivalence relation: States that two objects belong to the same equivalence class under a relation defined by the author. Example: The defined relation treats x and y as members of the same class.

Approximate or perturbed variant: A tilde placed over a symbol marks an approximate, sampled, perturbed, or transformed version. Example: The decorated value is a perturbed version of x.

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