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Concrete and abstract numbers
Recently I heard about the concepts of concrete number = numerus numeratus and abstract number = numerus numerans. See here. These seem to be mathematical...
Apr 14, 2026
Archive: News
news
Is the Laplace transform a linear operator?
Many sources online states that the Laplace transform $\mathcal{L}: V \to W, f(t) \mapsto F(s)$ is a linear operator For example: http://www2.fiu.edu/~ala...
Apr 14, 2026
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The surface of Aizawa attractor
Aizawa attractor creates a closed surface. Let's ignore the transient state in the beginning. I am wondering how to calculate its surface? I even don...
Apr 13, 2026
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Is this proportionality proof erroneous?
If $a$ is directly proportional to $b$ and also directly proportional to $c$, is it true that $a$ is directly proportional to $bc?$ (It seems like it is t...
Apr 13, 2026
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Volume of spherical shell with $dr$ thickness
Let's consider two spheres in the $(x,y,z)$ 3D-space, both centered in the origin: the inner with radius $r$ and the outer with radius $r + dr$. To c...
Apr 13, 2026
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Related Rates and Angle of elevation
I have been trying to wrap my head around related rates, which are super interesting but very difficult for me personally. Would anyone care to verify if ...
Apr 13, 2026
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Why is an ellipse, hyperbola, and circle not a function?
I am aware of the vertical line test. If you place a vertical line over a shape, and if it crosses more than once, it fails the vertical line test and is ...
Apr 13, 2026
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Expectation of a mixed random variable given only the CDF
I'm interested in the following question: Given only the cumulative distribution function $F(x)$ of a mixed random variable $X$, how does one proceed...
Apr 13, 2026
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What is the connection between linear algebra and geometry?
I am currently studying linear algebra. Yet, I found discussions about linear algebra usually explain things in a geometric fashion. I am quite confused o...
Apr 13, 2026
news
Evaluate the piecewise defined function
Evaluate the piecewise defined function at the indicated values. $f(x) = \begin{cases} 3 & \text{x≤5} \\ 5x-6, & \text{if x>5} \end{cases}$ $f(...
Apr 13, 2026
