Yes, that's true. But what I intended to convey was that it's very hard in the sense that we have only described a few dozen classes of transcendentals. So th

Yes, that's true. But what I intended to convey was that it's very hard in the sense that we have only described a few dozen classes of transcendentals. So the actual limiting factor has to be something other than this counting argument. The hard part is finding descriptions of transcendentals within the space of describable numbers.