In mathematics, the term

*infinity*, on its own, has no meaning. However, expressions such as*infinite sets*,*positive infinity*(denoted by +∞),*negative infinity*(denoted by −∞), etc. can be defined. The term “infinity” is used as an adjective to describe an object that has no quantity or size limit, such as a set of numbers, the set of points in a theoretical geometric plane and the number of decimals in an irrational number.### Symbol

The symbol “+∞” is read as “positive infinity”, and the symbol “−∞” is read as “negative infinity”.

### Examples

- The set of whole numbers (W) is an infinite set.
- The set of whole numbers less than 10 is the finite set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

### Educational note

Infinity, denoted by “∞”, is not a number, but a concept or a phenomenon. For example, we can say that the value of a variable *x* increases positively by taking on increasingly greater values; *x* is then said to approach infinity.

John Wallis (1616-1703), a student of William Oughtred, was the first to use the infinity symbol (∞). This symbol might be derived from an old Roman symbol for “one thousand”. Wallis used the infinity symbol in his work *Arithmetic Infinitorum*.