[linearrust]

> No; combining two countably infinite sets doesn't increase the cardinality of the result (because two is finite).

Agreed. But pi = 3.14...pi... isn't combing 2 infinite sets. It 'combining' infinite amounts of infinite sets and not in a linear fashion either.

You have to keep in mind the 2nd pi in the equation can be expanded to 3.14...pi...

pi = 3.14...pi... when expanded is pi = 3.14...(3.14...pi...)...

and you can keep expanding the inner pi forever.

> The digits would still be countably infinite.

How can you ever reach the first number after the inner pi in (pi = 3.14...pi...). Or put another way how do you get to the 4th '.'? You can't.

This is a classical example of countably infinite and a continuum.