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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
In its most common sense, rationality is the quality of being guided by reasons or being reasonable. [1] [2] [3] For example, a person who acts rationally has good reasons for what they do. This usually implies that they reflected on the possible consequences of their action and the goal it is supposed to realize.
Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. [10]
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
The definitions can be generalized to functions and even to sets of functions. Given a function f with domain D and a preordered set (K, ≤) as codomain, an element y of K is an upper bound of f if y ≥ f (x) for each x in D. The upper bound is called sharp if equality holds for at least one value of x. It indicates that the constraint is ...
The use of Unicode characters for blackboard bold is discouraged in English Wikipedia; instead, either the LaTeX rendering (for example <math>\mathbb{Z}</math> or <math>\Z</math>) or standard bold fonts should be used. As with all such choices, each article should be consistent with itself, and editors should not change articles from one choice ...
Reasonable may refer to: Reason, the capacity for rational thinking; Reasonable accommodation, an adjustment made in a system to accommodate an individual's need; Reasonable and non-discriminatory licensing, a licensing requirement set by standards organizations; Reasonable Blackman, a silk weaver in sixteenth-century England