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4h
reviewed Leave Open Impuls after collision
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reviewed Leave Open Rational Solution of a System of Linear Equations
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reviewed Leave Open When a system of rational linear homogeneous equations have complex solutions
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revised Naive proof that $\sum_{n=1}^{N-1}\cos(2\pi\frac{n}{N})=-1$
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answered Naive proof that $\sum_{n=1}^{N-1}\cos(2\pi\frac{n}{N})=-1$
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answered Proportionals and squares
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revised If $n > 0$ is an even composite integer, then $\varphi(n)$ is even?
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answered If $n > 0$ is an even composite integer, then $\varphi(n)$ is even?
7h
comment sequence: use of stirling formula
I did not want to bother with a tight bound, so gave away a lot in order to get what was needed quickly from the limit statement.
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comment What do double vertical lines mean?
Without the $^2$, it means the distance between the first term and the second. But they are considering the square of the distance, largely because squares of distances are better behaved than distances.
7h
comment Value of convergence of $\displaystyle\int\frac{\sqrt{x}}{1+x^2}$
@MhenniBenghorbal: You proved the convergence. In addition, the question asked for the value of the (original) integral.
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comment Value of convergence of $\displaystyle\int\frac{\sqrt{x}}{1+x^2}$
That's an upper bound. This definite integral, or related ones, has been on MSE before.
8h
comment Proof for divisibility?
A similar question, without the FTA request, was asked and answered yesterday. The FTA part is rather unnatural, one needs much less.
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comment sequence: use of stirling formula
You are welcome.
8h
comment sequence: use of stirling formula
However, one can view the process as shifting the burden. from proving the result directly by a Bernoulli inequality argument, to proving continuity of a certain two-variable function. The positive thing is that we need general continuity facts anyway, for other purposes.
8h
reviewed Leave Open Let (A,≼A) and (B,≼B) be partially ordered sets.
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comment sequence: use of stirling formula
I was using continuity of a two variable function.
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revised sequence: use of stirling formula
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comment sequence: use of stirling formula
I would rather give a more formal argument, which one can do using the Bernoulli Inequality. (I am assuming naturally that $K\ne 0$.) But in this case the intuition is right, and one can write a justification as follows: The function $y^x$ is continuous at $x=0$ for any $y\gt 0$.
9h
reviewed Leave Open How prove this integral inequality$ \int_{0}^{+\infty}\frac{1}{x^x}{\rm d}x<2 $