On: Pi calculation world record with over 202T digits

[thaumasiotes]

> If that was the case, wouldn't it mean that the digits of pi are not countably infinite but instead is a continuum.

No; combining two countably infinite sets doesn't increase the cardinality of the result (because two is finite). Combining one finite set with one countably infinite set won't give you an uncountable result either. The digits would still be countably infinite.

Looking at this from another direction, it is literally true that, when x = 1/7, x = 0.142....x.... , but it is obviously not true that the decimal expansion of 1/7 contains uncountably many digits.

[linearrust → thaumasiotes]

> 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.