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  2. Language of mathematics - Wikipedia

    en.wikipedia.org/wiki/Language_of_mathematics

    The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.

  3. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. [164] Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists.

  4. Probability interpretations - Wikipedia

    en.wikipedia.org/wiki/Probability_interpretations

    Epistemic or subjective probability is sometimes called credence, as opposed to the term chance for a propensity probability. Some examples of epistemic probability are to assign a probability to the proposition that a proposed law of physics is true or to determine how probable it is that a suspect committed a crime, based on the evidence ...

  5. Bayesian probability - Wikipedia

    en.wikipedia.org/wiki/Bayesian_probability

    Bayesian probability (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation [2] representing a state of knowledge [3] or as quantification of a personal belief.

  6. Glossary of mathematical jargon - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    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 ...

  7. Frequentist probability - Wikipedia

    en.wikipedia.org/wiki/Frequentist_probability

    Subjective (Bayesian) probability (a family of competing interpretations) considers degrees of belief: All practical "subjective" probability interpretations are so constrained to rationality as to avoid most subjectivity. Real subjectivity is repellent to some definitions of science which strive for results independent of the observer and analyst.

  8. Philosophy of mathematics - Wikipedia

    en.wikipedia.org/wiki/Philosophy_of_mathematics

    Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. [3] Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists.

  9. Constructivism (philosophy of mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constructivism_(philosophy...

    In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that

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