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.
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.