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divisbyzero.com | ||
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afnan.io
What is Infinity? We are going to start this post by trying to figure out what infinity is. What do you think of when you think of infinity? Most people know that it's this uncountable number or thing (or is it...?). There is no beginning or end, it just goes on forever. |
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thatsmaths.com
In last week's post, we defined an extension of parity from the integers to the rational numbers. Three parity classes were found --- even, odd and none. This week, we show that, with an appropriate ordering or enumeration of the rationals, the three classes are not only equinumerate (having the same cardinality) but of equal... |
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jaydaigle.net
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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statisticaloddsandends.wordpress.com
Let's say we have a convex, differentiable function $latex f: \mathbb{R}^p \rightarrow \mathbb{R}$ and that we want to minimize it. In this previous post, we saw that a gradient descent step at time $latex t$ (from point $latex \beta^t$) could be viewed as the minimizer of a quadratic approximation of $latex f$ at $latex \beta^t$:... |
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