# Why does using Plot3D with RealAbs cause a white space at kink but using Abs doesn't?

Consider the following plot:

Plot3D[RealAbs[(x-5)+y],{x,4.999,5.001},{y,0,0.001}]


The above plot has a white space where the derivative has a discontinuous jump (at $$y=5$$)

Plot3D[Abs[(x-5)+y],{x,4.999,5.001},{y,0,0.001}]


The white space is gone.

I understand that, according this answer, I can get rid of the whitespace by using the Exclusions option.

However, I am wondering why one command produces the whitespace by default and the other doesn't?

(my naive guess would be that because Abs thinks the argument is complex, that mathematica doesn't detect an exclusion at the kink)

• Neither of your plot commands are valid. Assuming that you included a range for y, the difference presumably has to do with the automatic detection for Exclusions. D[RealAbs[(x - 5) + y], y] evaluates; whereas, D[Abs[(x - 5) + y], y] is meaningless. Including the option Exclusions -> None will eliminate the white line. – Bob Hanlon Feb 8 at 20:43
• Sorry, I changed the question and didn't realize I deleted the y range. Ill add them back in. – user106860 Feb 8 at 21:24