Undefined (mathematics)

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages) This article may lack focus or may be about more than one topic. Please help improve this article, possibly by splitting the article and/or by introducing a disambiguation page, or discuss this issue on the talk page. (January 2015) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Undefined" mathematics – news · newspapers · books · scholar · JSTOR (January 2015) (Learn how and when to remove this message) (Learn how and when to remove this message)

In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values).^[1] The term can take on several different meanings depending on the context. For example:

• In various branches of mathematics, certain concepts are introduced as primitive notions (e.g., the terms "point", "line" and "plane" in geometry). As these terms are not defined in terms of other concepts, they may be referred to as "undefined terms".
• A function is said to be "undefined" at points outside of its domain – for example, the real-valued function ${\displaystyle f(x)={\frac {1}{x}}}$ is undefined for  ${\displaystyle x=0}$.
• In algebra, some arithmetic operations may not assign a meaning to certain values of its operands (e.g., division by zero). In which case, the expressions involving such operands are termed "undefined".^[2]