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Score of 2
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24 views

Unless I'm mistaken, there's the following derivation in Martin-Löf type theory showing that dependent functions which are pointwise judgmentally equal are themselves judgmentally equal: Consider ...
Score of 0
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44 views

I was just for fun thinking about the shape a wire takes when bent, expressed as a math function. setup The wire(length l, thickness t), when unbent is $x=±t/2$, for$ -L/2<y<L/2$ and $y=±L/2$ ...
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67 views

Let $F_h(x)$ be a function defined by a parametric integral: $$ F_h(x) = \int_{0}^{1} f(t,x,h) \, dt, $$ where $x$ is a real parameter where $F_h(1)$ is our goal. Suppose that by applying the Feynman ...
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42 views

I am sort of interested in set theory and idea of forcing and my math background is with no background in proof writing and I have done FOL only upto assignments, interpretation and free and unbounded ...
Score of -3
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47 views

Im a 22-year-old Venezuelan student (if you know the context of the country and the learning-teching problems, good). Recently I have had a great motivation to enter the world of math Olympiads, not ...
Score of 2
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28 views

The graph Laplacian, of course, comes up in a large variety of applied research, and it seems to me that one of the most important properties of the Laplacian is its spectrum. That is, mathematicians ...
Score of 0
2 answers
70 views

Background In the Mistborn TTRPG, success at a challenge is determined as follows. You roll $N$ six-sided dice, where $1 < N < 11$ (according to your stats, buffs, etc.), and you must surpass a ...
Score of 3
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132 views

Let us consider a prime number $p$ and three distinct positive integers $n_1<n_2<n_3$ less than $p$. Let us assume that the triple $(n_1, n_2, n_3)$ satisfies the following condition $$k+[kn_1]+[...
Score of 3
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29 views

I noticed an interesting property: For the circle $O: x^2+y^2=r^2$ and the parabola $C: y^2=2px$ ($p>0$), let their intersections be $P$ and $Q$. The tangent to the parabola at $P$ meets the circle ...
Score of 0
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18 views

For an $n$-simplex with vertices $A_0, \dots, A_n \subset \mathbb{R}^n$, suppose there exists a sphere of radius $R$ that is tangent to all its $\binom{n+1}{2}$ edge-lines. We can define signed ...
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61 views

I am trying to reconcile two definitions of tensors that I have encountered. The first definition I learned is the coordinate-transformation definition. In this definition, a tensor is an object that ...
Score of 1
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66 views

If an axiomatic system has Axioms A, B, C, ..., N, then we can form the conjunction $A \land B \land C \land \ldots \land N$ as a single axiom. How to deal with axiom schemas? Or is it impossible?
Score of 1
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46 views

I am trying to solve the following problem from Do Carmo's Riemannian Geometry: with $p(0) = q(0) = p$, $v(0) = w(0) = v$, and $V = \alpha'(0)$, $W = \beta'(0)$. Define an inner product on TM by $$ \...
Score of 2
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31 views

In Kedlayas lecture notes (https://kskedlaya.org/prismatic/sec_overview.html) about prismatic cohomology he introduces the ring of Witt vectors using $\delta$-rings via the fact that the Witt vector ...
Score of 1
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29 views

Let $G$ be a group object in an $\infty$-topos $\mathcal T$, and let $P \to X$ be a $G$-torsor as in the accepted answer by Daniël Apol to this question; equivalently, as in the answer, such a $G$-...

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