Ah! Now I see what your problem is: it all depends on whether the author requires that a<b or whether he is satisfied with theweakercondition that or even with no condition on a and b at all (like Rudin in his "Real & Complex Analysis").

If an author, such as Rudin in "Principles of Mathemacal Analysis", requires only , it follows that an interval like [a,a] is equal to the set which is clearly the same as . And the segment (a,a) would simply be the empty set.

Since Rudin is satisfied with the weaker condition , he follows the usage that I suggested was the more common. So it seems to me that your reading of Rudin's text is wrong.