Undefined (mathematics)

Common card · No. 208800

In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system. In practice, mathematicians may use the term undefined to warn that a particular calculation or property can produce mathematically inconsistent results, and therefore, it should be avoided. Caution must be taken to avoid the use of such undefined values in a deduction or proof. Whether a particular function or value is undefined, depends on the rules of the formal system in which it is used. For example, the imaginary number −1 is undefined within the set of real numbers. So it is meaningless to reason about the value, solely within the discourse of real numbers. However, defining the imaginary number i to be equal to −1, allows there to be a consistent set of mathematics referred to...

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