so i fucked up and have no idea how to do it. anyone wanna give a helping hand?
Im fucked up too
send help
I'll only help if you first tell me which part of the problem you're struggling with and explain to me all of your work and/or reasoning so far.
Say you've got a circuit with a lightbulb. Using P = IV for that lightbulb, an increased resistance results in less power and therefore not as bright of a bulb. But to me this doesn't make much sense because the visible light from a lightbulb is due to its resistance in the first place. So why would decreasing the resistance increase the amount of visible light generated?
>>7933992
i) well all points in K_0 will be in K, so i dont see whats there to prove
ii) because for all points x, y in K, there exists e>0 such that |x-y|=e
iii) fucked if i know
shameful bump
>>7933988
math.stackexchange.com is a better resource than /sci/ for upper-division and above math questions.
(i) obvious and routine
(ii) given any two different infinite sequences, you can write down an explicit open set separating them by finding the first n_k where they differ.
(iii) the set K is closed under multiplication by (i/3)
>>7934238
e: it is also closed under the operation T(z) = (i/3) + (i/3)z and i believe it is the smallest closed non-empty subset that contains (i/3) and is closed under iterative applications of T.
>>7933988
Using "of the form" here is a little vague, but I assume he means all the convergent sums of that form. By definition, such an infinite sum is the limit of its partial sums, so there is pretty much nothing to do for part (i).
