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This is not sharp; the gap between the functions is everywhere at least 1. Among the exponential functions of the form α x, setting α = e 2/e = 2.0870652... results in a sharp upper bound; the slightly smaller choice α = 2 fails to produce an upper bound, since then α 3 = 8 < 3 2. In applied fields the word "tight" is often used with the ...
[11] At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. [12] [6] The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. [13]
It seems to be this noncomprehension to comprehension which results in better recall. The essence of the aha feeling underlining insight problem solving was systemically investigated by Danek et al. [10] and Shen and his colleagues. [11] Recently an attempt has been made in trying to understand the neurobiological basis of Eureka moment. [12]
Microsoft Math was originally released as a bundled part of Microsoft Student. It was then available as a standalone paid version starting with version 3.0. For version 4.0, it was released as a free downloadable product [4] and was called Microsoft Mathematics 4.0.
Detemines the precision of a number. For example, for "4" it will return "0", for "4.567" it will return "3", and for "100" it will return "-2". The function attempts to parse the string representation of the number, and detects whether the number uses E notation. For this reason, when called from Lua, very large numbers or very precise numbers ...
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Among the 22 partitions of the number 8, there are 6 that contain only odd parts: 7 + 1; 5 + 3; 5 + 1 + 1 + 1; 3 + 3 + 1 + 1; 3 + 1 + 1 + 1 + 1 + 1; 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1; Alternatively, we could count partitions in which no number occurs more than once. Such a partition is called a partition with distinct parts. If we count the ...
The Eureka Stockade was a revolt in 1854 by gold miners against unjust mining license fees and a brutal administration supervising the miners. The rebellion demonstrated the refusal of the workers to be dominated by unfair government and laws. The Eureka Stockade has often been referred to as the "birth of democracy" in Australia. [11]