Gaussian Surfaces and infinite lines of charge

[JustStudying]

So I've been wondering..
from my previous post: https://www.physicsforums.com/showthread.php?p=4500082#post4500082

if we have a plane of infinite charge, then electric field does not depend on distance

however, for a infinite line of charge:
If we use a cylinder with radius 'r' as our gaussian surface then
the electric field has the equation

E = (charge density)/ (2∏ε * r)

which now depends on the radius of the cylinder.

This suggests that the electric field actually will have different values for different radius values
which (i feel) don't line up with the conclusion I reached in my first thread 'if we have a plane of infinite charge, then electric field does not depend on distance'

Any help?

 

[Simon Bridge]

Compare your reasoning in post #1 with the following:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html