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I'd like to ask you about the way of excluding just one point from this example:

myArg[z_] := Mod[Arg@z, 2 Pi]
RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}]

I want to exclude the $z \neq i$ $\mapsto$ point $(0,1)$.

Something like this:

enter image description here

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    $\begingroup$ Excluding a point would look the same as not excluding it. Perhaps you want to exclude a small region around the point of interest? If so, would just placing a white Point be an acceptable solution to your needs? $\endgroup$
    – rm -rf
    Oct 18, 2015 at 21:06
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    $\begingroup$ Hard to remove just one point, but here's a fake plot: RegionPlot[ y > x && myArg[x + I y] <= Pi && Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75] $\endgroup$ Oct 18, 2015 at 21:09
  • $\begingroup$ @R.M., I got your point. It's just for "educational usage" to show that $z \neq i$ is outside of the domain of a function. $\endgroup$ Oct 18, 2015 at 21:12
  • $\begingroup$ @J.M.isback., thank you so much. That's the most useful fake plot I've seen today ;). $\endgroup$ Oct 18, 2015 at 21:15
  • $\begingroup$ But, did you understand what I added to your code? $\endgroup$ Oct 18, 2015 at 21:18

1 Answer 1

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Credits to J. M. and R. M.

J. M. suggested drawing a surface outside the circle: a hole

Using the && operator he made the intersection of two sets:

RegionPlot[ y > x && myArg[x + I y] <= Pi 
&& Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75]

another hole

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    $\begingroup$ RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}, Epilog -> {White, AbsolutePointSize[6], Point[{0, 1}]}] $\endgroup$
    – Bob Hanlon
    Oct 18, 2015 at 22:24
  • $\begingroup$ @BobHanlon, thank you. Another useful example. $\endgroup$ Oct 18, 2015 at 22:30

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