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| bio | website | |
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| location | ||
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| visits | member for | 10 months |
| seen | 5 hours ago | |
| stats | profile views | 201 |
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6h |
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Can't understand homework assignment In fact, the common definition of "order" is always $p-1$ divided by the hint's definition of "order" and vice versa. |
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15h |
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Writing a sum as a fraction $i \ge i$? :) Anyway, you should note that $2f(x) = \sum (2x^3)^i$ and use the geometric series sum to simplify the second expression. For simplifying the first expression, I think you'll get a second geometric series after finding the common denominator, which will come from the $i=20$ term. |
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18h |
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How do I prove $\dim{U} = \dim{W}$ when… Hint The row-rank and the column-rank of any matrix are equal. |
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19h |
answered | Why don't we consider non-units as quadratic residues? |
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1d |
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Prime numbers; how to do this? From an algebraic point of view, $1$ doesn't admit a prime factorization :) When you look up the definitions of primes and unique factorization domains, you see that only non-invertible ring elements have a prime factorization. $1$ has the rare property of being an invertible integer, so it doesn't get to have a prime factorization. |
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1d |
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Is a series (summation) of continuous functions automatically continuous? Yeah, exchanging summation and integration always requires you to explain why it is allowed. Uniform convergence is a good justification. Sometimes you don't have uniform convergence and it is still justified, but you must then use more powerful tools, such as DCT (Dominated Convergence Theorem). And sometimes it is just wrong. |
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1d |
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Is a series (summation) of continuous functions automatically continuous? The sum of two continuous functions is continuous, therefore (you can show this by induction) the sum of any finite amount of continuous functions is continuous. |
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1d |
answered | Is a series (summation) of continuous functions automatically continuous? |
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May 20 |
answered | The harmonic conjugate of $\Im e^{z^2}$? |
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May 19 |
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Comparing the value of $\int _0 ^{\frac{\pi}{2}} x^n \sin^nx\,dx$ for different $n$ I don't agree, for $x = 1.5$ we have $x \sin x \approx 1.49$ and thus $(x \sin x)^n \to \infty$. |
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May 19 |
answered | Comparing the value of $\int _0 ^{\frac{\pi}{2}} x^n \sin^nx\,dx$ for different $n$ |
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May 19 |
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Comparing the value of $\int _0 ^{\frac{\pi}{2}} x^n \sin^nx\,dx$ for different $n$ What about the $x^n$ term which tends to infinity before $\frac \pi 2$? |
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May 16 |
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$i^{th}$ root(s) of unity (...which occurs if and only if $w$ is real and rational.) |
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May 15 |
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Meaning of $\log$ $\ln$ is always base $e$ but for $\log$ it depends on the context as I explained above. |
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May 15 |
awarded | Revival |
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May 7 |
awarded | Caucus |
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Apr 23 |
answered | Inner product in the Hilbert space |
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Apr 23 |
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Prove that $\sum_{k=0}^n{e^{ik^2}} = o(n^\alpha)$, $ \forall \alpha >0$ Related (I don't know much about this subject, though): en.wikipedia.org/wiki/Theta_function#Jacobi_theta_function |
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Apr 23 |
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Maximizing a convex function Maybe the first part holds with the additional condition $\varphi(0) = 0$? |
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Apr 22 |
reviewed | Approve suggested edit on How can I solve the equation $8=5x+2$? |
