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  2. One half - Wikipedia

    en.wikipedia.org/wiki/One_half

    One half is the rational number that lies midway between 0 and 1 on the number line. Multiplication by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling". A square of side length one, here dissected into rectangles whose areas are successive powers of ...

  3. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    Thus the fraction ⁠ 3 / 4 ⁠ can be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four). We can also write negative fractions, which represent the opposite of a positive fraction. For example, if ⁠ 1 / 2 ⁠ represents a half-dollar profit, then − ⁠ 1 / 2 ⁠ represents ...

  4. English numerals - Wikipedia

    en.wikipedia.org/wiki/English_numerals

    Alternatively, and for greater numbers, one may say for 1 ⁄ 2 "one over two", for 5 ⁄ 8 "five over eight", and so on. This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths"

  5. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

  6. Gill (unit) - Wikipedia

    en.wikipedia.org/wiki/Gill_(unit)

    [2] [3] Half of a gill is a jack, or an eighth of a pint. [4] But in northern England, a quarter pint could also be called a jack or a noggin, rather than a gill, and in some areas a half pint could be called a gill, particularly for beer and milk. [5] [6] [7]

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  8. Boy or girl paradox - Wikipedia

    en.wikipedia.org/wiki/Boy_or_Girl_paradox

    At least one of them is a boy. What is the probability that both children are boys? Gardner initially gave the answers ⁠ 1 / 2 ⁠ and ⁠ 1 / 3 ⁠, respectively, but later acknowledged that the second question was ambiguous. [1] Its answer could be ⁠ 1 / 2 ⁠, depending on the procedure by which the information "at least one of them is a ...

  9. Particular values of the gamma function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    It is unknown whether these constants are transcendental in general, but Γ(⁠ 1 / 3 ⁠) and Γ(⁠ 1 / 4 ⁠) were shown to be transcendental by G. V. Chudnovsky. Γ(⁠ 1 / 4 ⁠) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ(⁠ 1 / 4 ⁠), π, and e π are algebraically independent.