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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.
The terms themselves are undefined. Hilbert once remarked that instead of points, lines and planes one might just as well talk of tables, chairs and beer mugs. [ 3 ] His point being that the primitive terms are just empty shells, place holders if you will, and have no intrinsic properties.
Undefined value, a condition where an expression does not have a correct value; Undefined variable; Undefined, a function or variable lacking a declaration; Undefined, a variable lacking initialization; Undefined, an unavailable linker symbol (function, or global variable)
hot – higher order term. HOTPO – half or triple plus one. hvc ... undef – a function or expression is undefined. usc – upper semi-continuity. V
Hilbert's axiom system is constructed with six primitive notions: three primitive terms: [5] point; line; plane; and three primitive relations: [6] Betweenness, a ternary relation linking points; Lies on (Containment), three binary relations, one linking points and straight lines, one linking points and planes, and one linking straight lines ...
An undefined value must not be confused with empty string, Boolean "false" or other "empty" (but defined) values. Depending on circumstances, evaluation to an undefined value may lead to exception or undefined behaviour, but in some programming languages undefined values can occur during a normal, predictable course of program execution.
It starts with undefined terms and axioms, propositions concerning the undefined terms which are assumed to be self-evidently true (from Greek axios 'something worthy'). From this basis, the method proves theorems using deductive logic.