Recent content by experimentX

would this set be finite sub-cover of [0, 1] Sn={(1/n -ε, 2/n + ε): n ≥ 2} ? Choosing n > N ≥ 1/ε where ε > 0 would make it cover [0, 1]?

but this also covers (0,1), this would also be a finite sub cover of (0,1) making (0,1) compact. What I am asking is an example of sub covers of [0,1] that makes [0,1] compact while it does not make (0,1) compact

Then how could we say that cover of compact sets have finite sub-cover if we can't construct them. Shouldn't there be at least one example? I understand the proof given in my book but I can't visualize it.

I think I am not understanding the concept of compactness. Can anyone give me an example of a cover that contains finite sub-covers? for example:- G = {S1,S2, ... }, Sn={(1/n,2/n): n ≥ 2} is an example of cover of set (0,1) but it is an infinite collection.

\vec E = \frac{\hat r}{4 \pi r^2} \times \frac{Q}{\epsilon_0} \\ \vec E \cdot \hat r 4 \pi r^2 = \frac{Q}{\epsilon_0} \\ \text{Total Flux} = \frac{Q}{\epsilon_0} \\ \oint_s \vec E \cdot \hat n ds = \frac Q{\epsilon_0} Which is integral form of Gauss law.

I don't know where begin with or what to begin with ... I'm not looking for full answer either. I'm just looking for what to begin with and where to end.

Let an object of mass 'm' and volume 'v' be dropped in water from height 'h', and 'a' be the amplitude of the wave generated. What is the relation between 'a' and 'h'. How many waves are generated? What is the relation between relation between the amplitudes of successive waves?? Assume the...