text: The set of numbers for which a function is defined is called the domain of the function. If a number is not in the domain of a function, the function is said to be "undefined" for that number. Two common examples are , which is undefined for , and , which is undefined (in the real number system) for negative .
  In trigonometry
  In trigonometry, for all , the functions  and  are undefined for all , while the functions  and  are undefined for all .
  In complex analysis
  In complex analysis, a point  where a holomorphic function is undefined is called a singularity. One distinguishes between removable singularities (i.e., the function can be extended holomorphically to ), poles (i.e., the function can be extended meromorphically to ), and essential singularities (i.e., no meromorphic extension to  can exist).
  In computability theory
  Notation using ↓ and ↑
  In computability theory, if  is a partial function on  and  is an element of , then this is written as , and is read as "f(a) is defined."
  If  is not in the domain of , then this is written as , and is read as " is undefined".
  It is important to distinguish "logic of existence"(the standard one) and "logic of definiteness".