User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-27513631-20180807203627/@comment-30754445-20180807230927

No. That's precisely what "not continuous" means in this context:

If you have a sequence of ordinals  α1, α2, α3 ... then the limit of I(αn) is not equal to I(the limit of αn).

Inacessibles (and χ's) are weird that way.