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A single wave-shaped stroke marking equivalence, similarity or distribution.
Also known as: Similar to sign, Distributed as
A single tilde between two expressions is one of the most overloaded operators in mathematics. It marks asymptotic equivalence — two quantities whose ratio approaches one — and also similarity between geometric figures, an equivalence relation in the abstract, and in statistics the statement that a variable follows a distribution. Which meaning applies is decided by what sits on either side of it, and carrying the wrong one across from another field is the standard mistake.
Marks asymptotic equivalence in analysis: two quantities whose ratio approaches one as a limit is taken, which is a weaker statement than equality and a stronger one than a shared order of growth.
Contexts: Mathematics
Marks similarity between geometric figures — the same shape at a different size — which is the meaning most readers meet first and carry into contexts where it does not apply.
Contexts: Mathematics
States in statistics that a random variable follows a named distribution, so that the expression to its right is the name of a distribution rather than a quantity.
Contexts: Mathematics
A single horizontal stroke that curves up and then down again in one smooth wave, set on the middle of the line between two expressions.
One wave marks equivalence or distribution; two stacked waves mark approximation.
One is a mathematical operator and the other is a punctuation mark and diacritic; Unicode encodes them separately.