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  2. Wason selection task - Wikipedia

    en.wikipedia.org/wiki/Wason_selection_task

    The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966. [1][2][3] It is one of the most famous tasks in the study of deductive reasoning. [4] An example of the puzzle is: You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other.

  3. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠ ⁠ of two integers, a numerator p and a non-zero denominator q. [ 1 ] For example, ⁠ ⁠ is a rational number, as is every integer (for example, ). The set of all rational numbers, also referred to as " the rationals ", 2 the field of ...

  4. Dirichlet function - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_function

    In mathematics, the Dirichlet function[1][2] is the indicator function of the set of rational numbers , i.e. if x is a rational number and if x is not a rational number (i.e. is an irrational number). It is named after the mathematician Peter Gustav Lejeune Dirichlet. [3] It is an example of a pathological function which provides ...

  5. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  6. Vitali set - Wikipedia

    en.wikipedia.org/wiki/Vitali_set

    A Vitali set is a subset of the interval [,] of real numbers such that, for each real number , there is exactly one number such that is a rational number.Vitali sets exist because the rational numbers form a normal subgroup of the real numbers under addition, and this allows the construction of the additive quotient group / of these two groups which is the group formed by the cosets + of the ...

  7. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Repeating decimal. A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be ...

  8. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).

  9. Rationality - Wikipedia

    en.wikipedia.org/wiki/Rationality

    Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do, or a belief is rational if it is based on strong evidence. This quality can apply to an ability, as in a rational animal, to a psychological process, like reasoning, to mental states, such as ...

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