let S be the set of complex numbers z with magnitude less than R, and with imaginary part greater than 0. does the boundary of S include the values of z such that I(z)=0? (aka, is the “base” of the semicircle part of the boundary)
#boundary of a complex set shaped like a semicircle
devout sedge
dusky steppeBOT
magic valve
let S be the set of complex numbers z with magnitude less than R, and with imagi...
What are your thoughts on it?
devout sedge
What are your thoughts on it?
it would be natural to me to include said base, but it also seems to be a bit more complicated than i might expect to include this base
magic valve
You should follow your natural instincts
devout sedge
if it brings about any differences, this boundary is being found to take the integral over the boundary of that set as a contour
devout sedge
You should follow your natural instincts
is there no convention?
magic valve
wdym
devout sedge
because i imagine that the contour integral over the boundary with and without that base of the semicircle would have varying answers
devout sedge
wdym
when taking the boundary of a complex set such that it plots to. semicircle, is there a convention for whether or not one includes the flat portion of that semicircle in the boundary set
or would it be simply the curved portion
to me it seems that one would take it to be the former but it also seems that it would be a bit more convoluted to calculate that set
this is my exact set
the complex numbers such that the imaginary part is greater than 0 and the magnitude is between 0 and R exclusive
magic valve
because i imagine that the contour integral over the boundary with and without t...
So what would the boundary be without the base then?
magic valve
correct
devout sedge
so i suppose it would require that the base is included
magic valve
indeed
devout sedge
lest the set is not Closed
okay
Yay
well also not yay bc that makes it a bit harder
but Oh well
i got my answer. thank u
magic valve
$\partial X=\overline{X}\setminus X^{\circ}$
muted fulcrumBOT
SWR
magic valve
interior of the set
magic valve
no worries
devout sedge
thank u for ur help
magic valve
magic valve
.solved