Why equal sign wasn't used for boundaries for radius ($r

Question

Why boundaries for radius between internal and external conductor are set to
$a leq r < b$ instead of $a leq r leq b$?
Example: An air coaxial line made of copper ($μ sim μ_0$) is given. A constant current I flows through the inner conductor. The radius of the inner conductor is a and the outer conductor is of negligible thickness of radius b.

In other book boundaries are defined like this

garyp · Accepted Answer

At $r=a$ the function is continuous, so there is no ambiguity.  At $r=b$ the function is discontinuous, so you have to be more careful.  If it were $leq$ on both sides you would have two different answers for $r=b$
Edit after Comment
I think you can argue that it should be $r<b$ and $r>b$ since $r=b$ is a singularity and the value is therefore undefined. I like that version the best, but a physicist would pick one of the other versions because our brains are wired to think that there must be an answer at $r=b$.  Ask on the math Stackexchange forum.
Of course, all of this is like arguing over how many angels can dance on a pin. The abrupt discontinuity is an idealization that cannot occur in nature.

Why equal sign wasn't used for boundaries for radius ($r < b$) between internal and external conductor?

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