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In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. [1]Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system.
Alfred Tarski explained the role of primitive notions as follows: [4]. When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 January 2025. Look up undefined in Wiktionary, the free dictionary. Undefined may refer to: Mathematics Undefined (mathematics), with several related meanings Indeterminate form, in calculus Computing Undefined behavior, computer code whose behavior is not specified under certain conditions Undefined ...
A model for an axiomatic system is a well-defined set, which assigns meaning for the undefined terms presented in the system, in a manner that is correct with the relations defined in the system. The existence of a concrete model proves the consistency of a system [ disputed – discuss ] .
The strict definition of an undefined value is a superficially valid (non-null) output which is meaningless but does not trigger undefined behaviour. For example, passing a negative number to the fast inverse square root function will produce a number.
atan2(y, x) returns the angle θ between the positive x-axis and the ray from the origin to the point (x, y), confined to (−π, π].Graph of (,) over /. In computing and mathematics, the function atan2 is the 2-argument arctangent.
The plain meaning rule attempts to guide courts faced with litigation that turns on the meaning of a term not defined by the statute, or on that of a word found within a definition itself. According to the plain meaning rule, absent a contrary definition within the statute, words must be given their plain, ordinary and literal meaning.
In any topological space X, the empty set is open by definition, as is X. Since the complement of an open set is closed and the empty set and X are complements of each other, the empty set is also closed, making it a clopen set. Moreover, the empty set is compact by the fact that every finite set is compact. The closure of the empty set is empty.