No, because there's an uncountable infinity of uncountable infinities.
The class of all uncountable infinities is not a set, so it can't be an uncountable infinity.
This seems a bad way to think about things - except maybe for someone who's just been introduced to formal set theory - especially as proper classes are precisely those classes that are too big to be sets.
This is our monthly thread for collecting arbitrarily contrived scenarios in which somebody gets tortured for 3^^^^^3 years, or an infinite number of people experience an infinite amount of sorrow, or a baby gets eaten by a shark, etc. and which might be handy to link to in one of our discussions. As everyone knows, this is the most rational and non-obnoxious way to think about incentives and disincentives.