Infinity

About this character

The infinity symbol was introduced to mathematics in 1655 by the English mathematician John Wallis in his treatise De Sectionibus Conicis. He did not say where he got the shape; the standing hypothesis is that he adapted it from a late Roman numeral form of one thousand, sometimes written as a horizontally-flipped CIƆ. Within a generation it had displaced verbal phrasing in mathematical writing. The shape — a sideways figure-eight — is also called a lemniscate, from the Latin lemniscus, meaning a hanging ribbon. The curve U+221E is drawn to imitate is itself called the lemniscate of Bernoulli, an algebraic curve studied by Jacob Bernoulli forty years after Wallis.

In the Unicode standard, U+221E lives in the Mathematical Operators block and has the general category Sm (Symbol, Math). It is treated as a single symbol, not a number — a useful distinction, because NaN, +Infinity, and -Infinity in IEEE 754 floating point are bit patterns inside a number, not the literal character ∞. JavaScript's Infinity global is the IEEE positive infinity, written as a name rather than the symbol; the symbol is for human-readable display.

The infinity symbol has accumulated several distinct mathematical readings: a placeholder in limits (lim x → ∞), an upper bound in integrals (∫₀^∞), a cardinal in informal usage (though set-theoretic infinities use the Hebrew letter aleph ℵ), and a synonym for "very large" in everyday writing. There is a related but distinct codepoint U+29DC ⧜ INCOMPLETE INFINITY for an open variant, and U+29DD ⧝ TIE OVER INFINITY. For the directional infinities used in projective geometry, the convention is to write +∞ and −∞ with a separate sign character rather than encoding a signed infinity.