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Purpose of the Peano Axioms
Wikipedia says the Peano Axioms are a set of axioms for the natural numbers. Is the purpose of the axioms to create a base on which we can build the rest ...
Apr 14, 2026
Archive: News
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How to get a reflection vector?
I'm doing a raytracing exercise. I have a vector representing the normal of a surface at an intersection point, and a vector of the ray to the surfac...
Apr 14, 2026
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Determine all $2\times2$ matrices $A$ such that $A^2=0$.
This is from Lang's introduction to Linear Algebra page no 61. Determine all $2\times 2$ matrices $A$ such that $A^2 = 0$. Let $A=\begin{pmatrix} a &...
Apr 14, 2026
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How to derive the divergence theorem from the General Stokes theorem?
So, given the generalized Stokes theorem: $$\int_{\partial M} \omega = \int_M d\omega$$ where M is an n-dimensional surface and $\omega$ is a p-form on M ...
Apr 14, 2026
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Find the remainder when $1!$+$2!$+$3!$....$49!$ is divided by 7?
what is the remainder when 1!+2!+3!+4!+⋯+49! is divided by 7? MyApproch: By taking individual numbers as ($1$!+$2$!+$3$!+$4$!+⋯+$49$!)/$7$ I get $1$+$2$+$...
Apr 14, 2026
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Condition for an equation to be an identity
For some equation to be an identity, should the LHS and RHS have same domain (given equality holds for all values of x). For example, are both of these an...
Apr 14, 2026
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Proof of e as a limit
I'm reading this text: A few questions: What's the importance of them going from $h$ to $x$ in the first line? What is the difference? How did t...
Apr 14, 2026
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How to solve : $\,8^x=6x$
I am stuck on the following problem which one of my friends gave me: Solve : $\,8^x=6x$. MY ATTEMPTS: We see that $$8^x=6x \implies 2^{3x}=6x.$$ Now I am ...
Apr 14, 2026
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What is the defining feature of a twice differentiable function?
For example $f(x) = x^2$ is twice-differentiable. What special properties does $f(x) = x^2$ hold over a function that is differentiable but not twice-diff...
Apr 14, 2026
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Find two different rules for one sequence $2, 4, 8, \ldots$
Question: The first three terms of a sequence are given. $2, 4, 8...$ Write two different rules for continuing the sequence. Give the next two terms for e...
Apr 14, 2026
