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The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.
The relationship x precedes y is written x ≺ y. The relation x precedes or is equal to y is written x ≼ y. The relationship x succeeds (or follows) y is written x ≻ y. The relation x succeeds or is equal to y is written x ≽ y. [citation needed]
In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...
Yamaha V-Max and VMAX, motorcycles; EMC Symmetrix, VMAX Series, a data storage product line from EMC Corporation; Maximum Velocity (V-Max), an Italian movie; Vmax cinemas of Event Cinemas and Village Cinemas, features larger screens and enhanced visual and audio quality; VMaX (Véhicule Manœuvrant Expérimental) a French hypersonic glide vehicle
It is always true that the left-hand side is at most the right-hand side (max–min inequality) but equality only holds under certain conditions identified by minimax theorems. The first theorem in this sense is von Neumann 's minimax theorem about two-player zero-sum games published in 1928, [ 2 ] which is considered the starting point of game ...
The Yamaha XMAX is a series of maxi-scooters manufactured by Yamaha Motor Company since 2006. [1]It is available in four engines (the 125, 250, 300 and the 400 cm3), and is enjoying strong commercial success in Europe.
In mathematics, an absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite.
Basic Inc. v. Levinson, 485 U.S. 224 (1988), was a case in which the Supreme Court of the United States articulated the "fraud-on-the-market theory" as giving rise to a rebuttable presumption of reliance in securities fraud cases.