Infinity sign

The infinity symbol ∞ (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity.

The shape of a sideways figure eight has a long pedigree; for instance, it appears in the cross of Saint Boniface, wrapped around the bars of a Latin cross. However, John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his De sectionibus conicis. Wallis did not explain his choice of this symbol, but it has been conjectured to be a variant form of a Roman numeral for 1,000 (originally CIƆ, also CƆ), which was sometimes used to mean "many", or of the Greek letter ω (omega), the last letter in the Greek alphabet.

Leonhard Euler used an open variant of the symbol in order to denote "absolutus infinitus". Euler freely performed various operations on infinity, such as taking its logarithm. This symbol is not used anymore, and is not encoded as a separate character in Unicode.

In old times when most typesetting was by hand with lead type, the infinity symbol was easily made by typesetting an 8 rotated 90 degrees.

In mathematics, the infinity symbol is used more often to represent a potential infinity, rather than to represent an actually infinite quantity such as the ordinal numbers and cardinal numbers (which use other notations). For instance, in the mathematical notation for summations and limits such as

the infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large (towards infinity) rather than actually taking an infinite value.

In areas other than mathematics, the infinity symbol may take on other related meanings; for instance, it has been used in bookbinding to indicate that a book is printed on acid-free paper and will therefore be long-lasting.

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