Recent content by FeDeX_LaTeX

Thanks for the automated response. I posted the same question on MathSE, and was told that the manipulation is correct as long as everything converges, although one should note that the convolution is on \mathbb{Z} rather than on \mathbb{R}. The only question I have left is whether that means I...

Homework Statement [/B] Suppose we have a 2\pi-periodic, integrable function f: \mathbb{R} \rightarrow \mathbb{C} whose Fourier coefficients are known. Parseval's theorem tells us that: \sum_{n = -\infty}^{\infty}|\widehat{f(n)}|^2 = \frac{1}{2\pi}\int_{-\pi}^{\pi}|f(x)|^{2}dx, where...

Thanks to the advice posted in this thread, I have now gone a full year without being ill, for the first time in my life! Now aiming to avoid illness for the rest of the calendar year.

I heard this phrase all the time back at school. (I'm from London.)

Almost. Are you sure the inverse of 6 is 1? Can two elements have the same inverse?

I don't agree with the bolded. Is the product of 1 and 6 the identity element? Correct. Such an element is called a generator of G.

This is easiest to do if you instead try showing that, if E_i are open sets, where 1 \leqslant i \leqslant n, then \bigcap_{i=1}^{n} E_{i} is open, which pretty much follows from the definition of an open set. You can then take complements and you're done.

You've pretty much already got the answer. Just expand that last line and re-arrange.

Hi there!

Did you hear about the constipated mathematician? He worked it out with a pencil.

Needs no explanation. :)

Agreed, those options are wrong (and your solution is correct). There's probably a typo in either B or C.

Thanks for all of your replies. I've bought one of those alcohol-based sanitisers as someone suggested, and I'm getting into the habit of washing my hands more frequently, and trying to get into the habit of a more regular sleeping pattern and better exercise. I've decided to go to the...

The negative sign makes it so that the stated number isn't real.

What's the derivative of sine? Can you see a neat substitution you could make?