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Circle integral in polar coordinates
I know how to integrate and deduce the area of a circle using vertical "slices" (dx). However, I wanted to know how to solve the problem another way: slic...
Apr 17, 2026
Archive: News
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Algebraic definition of ringoid
Category theory has the concept of a groupoid and this is a different concept from the use of the word groupoid to refer to a magma. Wikipedia gives an al...
Apr 17, 2026
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Proof of Multivariable Implicit Differentiation Formula
If the equation $F(x,y,z)=0$ defines $z$ implicitly as a differentiable function of x and y, then by taking a partial derivative with respect to one of th...
Apr 17, 2026
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Probability of getting heads given that first flip was a head?
What's the probability of getting heads on the second toss given that the first toss was a head. (Trying to refresh my probability a bit). I've ...
Apr 17, 2026
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Proving the Division Algorithm using induction
Let $n \in \mathbb{N}$. For every $m \in \mathbb{Z}$, there exist unique $q, r \in \mathbb{Z}$ such that $ m = qn+r$ and $0 \le r \le n-1$. We call $q$ th...
Apr 17, 2026
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Dirac Delta Function of a Function
I'm trying to show that $$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$ Where $a_{i}$ are the roots of...
Apr 17, 2026
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Intersection of Two Planes
I keep hearing different answers for what the intersection of two planes is. I believe it is a line, but it can also be a plane IF the two planes are not ...
Apr 17, 2026
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Is there a problem when defining exponential with negative base?
Well, this question may seem silly at first, but I'll make my point clear. Suppose $n \in \Bbb N$ and suppose $a \in \Bbb R$ is any number. Then the ...
Apr 17, 2026
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Find set of vectors orthogonal to $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$
$\mathbf{Question:}$ Find set of vectors orthogonal to $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$ $\mathbf{My\ attempt:}$ The vector is in $R^3$ so we...
Apr 17, 2026
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What exactly is an endomorphism?
As I understand it, given a set $A$, an endomorphism is a function $f$ which maps $A$ to itself. $f : A \rightarrow A$ So, for a concrete example, would w...
Apr 17, 2026
