User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-24725252-20171219225952

What is the limit of the ordinals with levels 400, 490, 499, 499.9, 499.99, 499.999.... Because this is a countable sequence, and the levels of theese ordiansl are countable, the limit of them is countable, unless you don't believe in Countable Choice. That menas the scale must be discontinous and exclude uncountably many ordinals because you said 500 was the first uncountable ordinal.