complexanalysisiii blogspot.com

Complex Analysis III

Sunday, March 18, 2007. Examples of diffcont at a point. Cont only at a point. Fz z if z irrational and - z if z is irrational. Rotate usual function. Note that if z 0 0 then lim z- z 0fz DNE. Given epsilon 0 consider fz-fz 0 for z in B epsilon,z 0. If z 0 irrat then z- z 0 along rational approximations gives fz-fz 0 2 z 0 epsilon -- 0 as z- z 0. So f is not cts at z 0. As z- 0 fz-f0 z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures x I think. It includes fou.
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Complex Analysis III

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Sunday, March 18, 2007. Examples of diffcont at a point. Cont only at a point. Fz z if z irrational and - z if z is irrational. Rotate usual function. Note that if z 0 0 then lim z- z 0fz DNE. Given epsilon 0 consider fz-fz 0 for z in B epsilon,z 0. If z 0 irrat then z- z 0 along rational approximations gives fz-fz 0 2 z 0 epsilon -- 0 as z- z 0. So f is not cts at z 0. As z- 0 fz-f0 z 0 - 0. So cts at 0. Diff only at a pt. Example in lectures x I think. It includes fou.

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This web page complexanalysisiii.blogspot.com states the following, "Sunday, March 18, 2007." We saw that the webpage said " Examples of diffcont at a point." It also said " Cont only at a point. Fz z if z irrational and - z if z is irrational. Note that if z 0 0 then lim z- z 0fz DNE. Given epsilon 0 consider fz-fz 0 for z in B epsilon,z 0. If z 0 irrat then z- z 0 along rational approximations gives fz-fz 0 2 z 0 epsilon -- 0 as z- z 0. So f is not cts at z 0. As z- 0 fz-f0 z 0 - 0. Diff only at a pt. Example in lectures x I think."

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