> But there are uncountably many finite collections of symbols.
As others have pointed out, that depends on how big the set of possible symptoms are.
If the set is finite, then there are a countable number of finite collections (the countable union of countable sets is still countable).
If the set is countably infinite, then there are still countably many finite collections.[1]
If the set is uncountably infinite, then you're right. However, the author is probably talking about all symbols known to humanity, which clearly is not only not uncountable, but it is finite.
As others have pointed out, that depends on how big the set of possible symptoms are.
If the set is finite, then there are a countable number of finite collections (the countable union of countable sets is still countable).
If the set is countably infinite, then there are still countably many finite collections.[1]
If the set is uncountably infinite, then you're right. However, the author is probably talking about all symbols known to humanity, which clearly is not only not uncountable, but it is finite.
[1] https://math.stackexchange.com/questions/200389/show-that-th...