Wiktionary
a. 1 (context mathematics computing theory English) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included. 2 (context mathematics English) (''of a WFF'') logically independent from the axioms of a given theory; i.e., that it can ''never'' be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (''Note:'' this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)
Wikipedia
Undecidable may refer to: __NOTOC__
- Undecidable problem in computer science and mathematical logic, a decision problem that no algorithm can decide, formalized as an undecidable language or undecidable set
- "Undecidable" is sometimes also used as a synonym of independent, something that can neither be proved nor disproved within a mathematical theory
- Undecidable figure, a two-dimensional drawing of something that cannot exist in 3d, such as appeared in some of the works of M. C. Escher
Usage examples of "undecidable".
Hassan, I believe the creatures in there are creatures of mathematics - swimming in a Godelian pool of logic, growing, splitting off from one another like amoebae as they absorb undecidable postulates.
The new statement was undecidable, not deducible from the set within him.
What it says is that all consistent axiomatic systems of number theory include undecidable propositions.
This was undecidable, within logically simpler systems like set theory.
This was undecidable, within logically simpler systems like set theory: additional assumptions had to be made.