GEdgar
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 9h comment pointwise convergence of a filter on $\mathbb{R}^\mathbb{R}$ Do you know what it means for a sequence of functions to converge pointwise? This is what happens when you adapt that definition to convergence of filters. I think your difficulty is probably not pointwise convergence, but instead convergence of filters in general. 9h comment $\forall x\in\mathbb{R},,$ if $x^{2}$ is rational, then $x$ is rational. But you should include the question within the question box, not merely in the subject line. 9h comment Is $2^{\aleph_0} = \aleph_1$? It is truly a common false belief. (Unlike some of the others in that thread.) It has appeared in "popular" math books by non-mathematicians. 9h comment Prove that ($\mathbb{R}$, $\le$) is a partial order In a total order, each pair of elements is comparable (either $x \le y$ or $y \le x$ or both). In a partial order you can have a pair of elements incomparable (neither $x \le y$ nor $y \le x$). 18h comment Working out $\tan x$ using sin and cos expansion An alternate way to write long division 18h comment Working out $\tan x$ using sin and cos expansion not an answer to the question 1d comment Why is $\int\limits_{\gamma} \frac{1}{z-1} \neq 2\pi i$, $\gamma = \{z : \lvert z \rvert = 1\}$? The path $\gamma$ in Cauchy's formula should surround $a$. Not pass through it as in your case. 1d comment When is $n\choose k$ a multiple of $n$ $\binom42 = 6$ is the first counterexample. 1d comment Solve the differential equation by variation of parameters. $y'' + y = \sin x$ Show your work first. Then we can tell what your confusion is. Start with: what is the method of variation of parameters? Even if the question is "put on hold", you can still improve it, and then it may be re-instated. 1d revised Improper integral Riemann sum limit in the derivation of Fourier series to Fourier transform edited body 1d revised Improper integral Riemann sum limit in the derivation of Fourier series to Fourier transform added 105 characters in body 1d answered Improper integral Riemann sum limit in the derivation of Fourier series to Fourier transform 1d comment How to solve the functional equation $f(2x) = (e^x+1)f(x)$? To show $g$ is constant, you need to know $g(0)$ exists. But your definition of $g$ does not show that. 1d comment Show that the sequence $a_n=\frac{\sin(n)}{2+\cos(n)}$ has a convergent subsequence. To make $U_n/V_n$ as large as possible (when they are positive), make $U_n$ as large as possible, and make $V_n$ as small as possible. 1d comment How can I split this into its' real and imaginary parts, and simplify? Can you show your finial numerator is (in absolute value) at most $4$? 1d comment Swapping series and linear operators Use the definition of "continuous". And the defintion of "convergence" for the series. (You also need the definition of "linear"). 1d comment Evaluating norm of the operator Look at the line you wrote there. Can you choose $x_n$'s so that all of those ${}\le$'s become ${}=$'s? If you can, you are done. If you can't it will show you how to get a better estimate. 1d comment ((a ⇔ b) ⇒ c) ⇔ (a ⇔ (b ⇒ c)) tautology, contradiction, or neither? You have a start. This T shows it is not a contradiction. Now (as the others said) do some more rows of the truth table. If you get an F in some row, it will show this is not a contradiction. You can stop as soon as that happens (and answer "neither"). If you do all 8 rows, and always get T, then it would show this is a tautology. 2d comment Proving there is no continuous function $f: [0, 1] \rightarrow \mathbb R$ that is onto Do you have a theorem about continuous functions on $[a,b]$? 2d comment What is the difference between a parametric equation and cartesian equation? Cartesian equation example: $x^2+y^2=1$. Parametric equation example: $x = \cos t, y = \sin t, 0 \le t < 2\pi$. That extra variable $t$ is a parameter.