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mattbaker.blog | ||
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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jaydaigle.net
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| | | | | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. | |
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thatsmaths.com
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| | | | | The numbers are usually studied in layers of increasing subtlety and intricacy. We start with the natural, or counting, numbers $latex {\mathbb{N} = \{ 1, 2, 3, \dots \}}&fg=000000$. Then come the whole numbers or integers, $latex {\mathbb{Z} = \{ \dots, -2, -1, 0, 1, 2, \dots \}}&fg=000000$. All the ratios of these (avoiding division... | |
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booksandpictures.wordpress.com
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| | | Cat is mine, dog is not. | ||
