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You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses ...
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.
[7] Three days before the deadline, the Evernote Corporation announced that users could sync their existing Fotopedia material with Evernote before the shutdown, free of charge. [ 8 ] The Archive Team made a backup available on archive.org. [ 9 ] [ 10 ] However, the pictures are not directly displayed, but assembled within archive files that ...
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
A first edition forms part of the Crawford Collection, housed at the Royal Observatory, Edinburgh. [101] The Uppsala University Library owns a first edition copy, which was stolen in the 1960s and returned to the library in 2009. [102] The Folger Shakespeare Library in Washington, D.C. owns a first edition, as well as a 1713 second edition.
A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.
At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point. (In fact, one can show that f takes both positive and negative values in small neighborhoods around (0, 0) and so this point is a saddle point of f .)
The Second Temple (Hebrew: בֵּית־הַמִּקְדָּשׁ הַשֵּׁנִי Bēṯ hamMīqdāš hašŠēnī, transl. 'Second House of the Sanctum' ) was the reconstructed Temple in Jerusalem , in use between c. 516 BCE and its destruction in 70 CE.
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