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| bio | website | hewwolff.org |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 11 months |
| seen | yesterday | |
| stats | profile views | 72 |
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Apr 10 |
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Quotient function Hint: try to define $h$ and show that it's unique; then show that it's continuous. |
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Apr 10 |
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Universal property characterizing $\Bbb R$ It's also probably the only object in that category, depending on how you define "complete". |
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Apr 10 |
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Let $f(x,y)=\frac{x^3-y^3}{x^2+y^2}$. Is f differentiable in $(0,0)$? @Babak: heck, I don't know, but they did ask about it. |
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Apr 10 |
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Let $f(x,y)=\frac{x^3-y^3}{x^2+y^2}$. Is f differentiable in $(0,0)$? Not sure about differentiability, but it's clear that $f$ is a linear function from $\mathbb{R}^2$ to $\mathbb{R}$ if we define $f(0, 0) = 0$. Just compare $f(kx, ky)$ to $f(x, y)$. |
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Apr 10 |
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apollonian circles: why are radius and center dual? I don't understand what the question is. Are you asking for a proof of that equation (for both centers and radii)? Have you looked at "Wilks et al."? |
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Apr 10 |
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2 times differentiable functions with compact support @gerw, but surely a polynomial would not be compactly supported (and would be infinitely differentiable). |
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Apr 6 |
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Number of pairs of points whose distance is one When you say $XA+XC+XB+XC$, I think the last one should be $XD$, not $XC$. And when you say $(XA+AB)+(XC+XD)$, I think the second one should be $XB$, not $AB$. Nice argument! |
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Feb 8 |
answered | Why is there no contradiction by construction of alternating knots? |
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Feb 8 |
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Is Turing-completeness decidable? I think you would need a well-defined way to encode a model of computation as input for (say) a Turing machine. Any thoughts on how you would do that? |
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Jan 23 |
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Why does a circle cut a torus into an annulus? Rolfsen, in section 2C of Knots and Links, classifies 1-knots in the torus basically by proving this result. It's not a long proof, but I wouldn't call it trivial either. |
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Jan 17 |
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Can someone explain the precise difference between of direct sum and direct product of groups? Also, in the category of abelian groups, the direct sum is the coproduct whereas the direct product is the product. Roughly speaking, this means that it's easy to construct maps from the coproduct but to the product. |
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Jan 16 |
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Direct product of group order 2 That's a good start. Your list of the elements is correct, but what are the subgroups of $P \times P$? |
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Jan 16 |
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Existence of a measure-preserving mapping between two given measure spaces? Sorry, you are correct. I have attempted to fix my example. |
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Jan 16 |
revised |
Existence of a measure-preserving mapping between two given measure spaces? fixed problem with definition of measure-preserving mapping |
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Jan 16 |
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How do you call a 3d convex shape made of 8 arbitrary points? A convex polytope with 8 vertices will generally have triangular faces, not quadrilateral faces, so it will be quite different from a box. I don't think it has a name, although a 3-D polytope with 4 vertices is called a 3-simplex. |
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Jan 16 |
revised |
Existence of a measure-preserving mapping between two given measure spaces? removed bad example |
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Jan 16 |
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Existence of a measure-preserving mapping between two given measure spaces? Right you are, I'll remove that. |
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Jan 16 |
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Limiting search space around line segment via rectangular buffer This sounds like a question for Stack Overflow with an "algorithms" tag, not really a math question. I think you will also want to add more detail about what you want to do, because I don't understand it. |
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Jan 16 |
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Existence of a measure-preserving mapping between two given measure spaces? Sorry, I know nothing about KET, just some very basic measure theory. See if this helps: $\Omega_1$ is the integers, $F_1$ is the set of all subsets of the integers, and $\mu_1$ takes every set to the size of that set. Check that this defines a measure. Similarly for $i = 2$, except that $\mu_2$ is twice as large. Then pick a point (say $0$) and think about the measure of that point and the measure of its image. |
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Jan 16 |
revised |
Existence of a measure-preserving mapping between two given measure spaces? added example |
