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In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined , ill defined or ambiguous . [ 1 ]
It remains an open question as to whether there exists a more powerful definition of 'well-defined' that is able to capture both computable and 'non-computable' statements. [note 1] [8] Some examples of mathematical statements that are computable include: All statements characterised in modern programming languages, including C++, Python, and ...
For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an effective method, an algorithm can be expressed within a finite amount of space and time [3] and in a well-defined formal language [4] for calculating a function. [5]
Well-Ordered: The exact order of operations performed in an algorithm should be concretely defined. Feasibility: All steps of an algorithm should be possible (also known as effectively computable). Input: an algorithm should be able to accept a well-defined set of inputs.
The definition of a formula comes in several parts. First, the set of terms is defined recursively. Terms, informally, are expressions that represent objects from the domain of discourse. Any variable is a term. Any constant symbol from the signature is a term
Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions. These might be regarded as 'natural' problems in that there are physical processes modelled by these problems. Problems that are not well-posed in the sense above are termed ill-posed. A ...
In algorithmic inference, a well-behaved statistic is monotonic, well-defined, and sufficient. In Bézout's theorem, two polynomials are well-behaved, and thus the formula given by the theorem for the number of their intersections is valid, if their polynomial greatest common divisor is a constant.
Although the term well-behaved statistic often seems to be used in the scientific literature in somewhat the same way as is well-behaved in mathematics (that is, to mean "non-pathological" [1] [2]) it can also be assigned precise mathematical meaning, and in more than one way. In the former case, the meaning of this term will vary from context ...