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Questions regarding the well-definedness of a function often arise when the defining equation of a function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives. This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result ...
For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P ( n ) represent " 2 n − 1 is odd": (i) For n = 1 , 2 n − 1 = 2(1) − 1 = 1 , and 1 is odd, since it leaves a remainder of 1 when divided by 2 .
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The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
A small torrent file is created to represent a file or folder to be shared. The torrent file acts as the key to initiating downloading of the actual content. Someone interested in receiving the shared file or folder first obtains the corresponding torrent file, either by directly downloading it or by using a magnet link. The user then opens ...
Berkshire Hathaway (NYSE: BRK.A)(NYSE: BRK.B) owns a stock portfolio worth roughly $300 billion with about four dozen individual stocks in it. Legendary stock-picker Warren Buffett himself hand ...
5. Take your health seriously — it’s expensive. Health care costs have hit many baby boomers hard, especially as they’ve gotten older. Many learned (sometimes too late) that skipping routine ...
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