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The number of grains of wheat on the second half of the chessboard is 2 32 + 2 33 + 2 34 + ... + 2 63, for a total of 2 64 − 2 32 grains. This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains one more grain than the entire first half.
In Hong Kong, one picul was defined in Ordinance No. 22 of 1844 as 133 + 1 ⁄ 3 avoirdupois pounds. [4] The modern definition is exactly 60.478982 kilograms. [2] The measure was and remains used on occasion in Taiwan where it is defined as 60 kg. [9] The last, a measure of rice, was 20 picul, or 1,200 kg. [10]
Mathematical fallacy. In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known ...
Euler's identity. In mathematics, Euler's identity[ note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
[1] The long or imperial hundredweight of 8 stone or 112 pounds (50.80 kg) is defined in the British imperial system. [2] Under both conventions, there are 20 hundredweight in a ton, producing a "short ton" of 2,000 pounds (907.2 kg) and a "long ton" of 2,240 pounds (1,016 kg).
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A grain is a unit of measurement of mass, and in the troy weight, avoirdupois, and apothecaries' systems, equal to exactly 64.798 91 milligrams. It is nominally based upon the mass of a single ideal seed of a cereal. From the Bronze Age into the Renaissance, the average masses of wheat and barley grains were part of the legal definitions of ...
Rice's theorem puts a theoretical bound on which types of static analysis can be performed automatically. One can distinguish between the syntax of a program, and its semantics . The syntax is the detail of how the program is written, or its "intension", and the semantics is how the program behaves when run, or its "extension".