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4h
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awarded | Enlightened |
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4h
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awarded | Nice Answer |
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16h
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comment |
What is the identity of this zeta function? Are you sure you didn't miscopy the first sum? It seems that it should be $\sum_{m=0}^\infty$ instead of $\sum_{m=1}^n$; in that case, this would be the actual Riemann zeta function, as the blog seems to be indicating and as Mathematica can verify. |
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19h
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comment |
Using Residue Theorem for functions with removable singularities Yes, that's correct :) Alternatively you can consider the residue at $z=0$ as well, but that residue will equal $0$. |
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20h
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awarded | riemann-zeta |
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1d
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answered | Is there a reason why the Maclaurin coefficients of the Riemann zeta function are asymptotically close to -1? |
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1d
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revised |
The probability of multiplicity of the sum of the dice changed to inclusive pronouns |
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1d
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revised |
Prof. Knuth lecture about $ \pi $ and random maps deleted 4 characters in body |
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1d
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revised |
Knights, Knaves, and Spies changed to inclusive language |
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2d
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comment |
Continuity of the multiplication and inversion in the definition of topological group No, they are the same for finite cartesian products. |
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2d
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comment |
Approximating the Prime Counting Function as $\pi(x) \approx \frac{x^2}{\ln\left(\Gamma(x+1)\right)}$ I doubt there's any useful connection with entropy. The mathematics is just about the functions themselves, and these particular functions are okay but not great at approximating $\pi(x)$. |
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2d
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answered | Given the primes, how many numbers are there? |
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2d
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comment |
Continuity of the multiplication and inversion in the definition of topological group Yes, every open set in a product topology contains a product of open sets—I recommend rereading the definition of the product topology to see why. As for (3): any continuous function $f$ from a space to itself such that $f\circ f$ is the identity is always a homeomorphism, so neighbourhoods are preserved. |
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2d
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comment |
Continuity of the multiplication and inversion in the definition of topological group Question 1 seems equivalent to asking whether every open set in the product topology is the product of open sets of the factors; this answer is definitely no (there are lots of open sets in $\Bbb R^2$ that aren't open rectangles, for example). |
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2d
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comment |
Given the primes, how many numbers are there? @Charles If you're going to make this distinction between a prime/element and its valuation, then you'll need to be more specific about your counting functions. Are you counting primes up to $x$, or primes whose valuations go up to $x$? elements up to $x$, or elements whose valuations go up to $x$? Is an element a product of primes or a product of valuations? If the former, is the valuation of a product of primes equal to the product of the valuations of the primes? |
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2d
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comment |
Given the primes, how many numbers are there? Is it the case that the “primes” are literally the real numbers of the form $\frac p2$ where $p$ is an odd prime? so that for example $(\frac32)^2 \frac52$ is one the elements? I too am trying to make sense of “valuations”. |
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Jul
17 |
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How to give this sum a bound? @jjagmath Good point, presumably the OP needs to add $x\ne 0$ and $y\ne 0$ to the conditions of summation. |
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Jul
17 |
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answered | Compute the value of a double sum |
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Jul
17 |
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comment |
Resolution to the "Ladder Movers' Problem"? Presumably the OP's main question is the last sentence; they could edit to clarify that. OP, maybe you could be more specific about what you mean by "canonical resolution" as well. |
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Jul
17 |
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Shall proofs be externalised? I wouldn't say that one option is always better than the other. The best thing to do (which you are already doing!) is to weigh the pros and cons of both options, and hybrid options such as those suggested in previous comments. |