A mathematical zen koan

[mr3000]

Say you have a dot. That dot explodes into an infinite number of dots. Each of those dots explode into a new infinite number of dots. Each of those dots explode into a new infinite number of dots, ad infinitum.

How many dots do you have in total?

 

[Hornbein]

Say you have a dot. That dot explodes into an infinite number of dots. Each of those dots explode into a new infinite number of dots. Each of those dots explode into a new infinite number of dots, ad infinitum.

How many dots do you have in total?

A shitload.

 

[Baluncore]

How many dots do you have in total?

∞^∞ = ∞

 

[Borek]

My knowledge about infinities is infinitesimally small, but there is a chance answer depends on what kind of infinity you started with. Was it $\aleph_0$? $\aleph_1$? Something else?

 

[Hornbein]

Say you have a dot. That dot explodes into an infinite number of dots. Each of those dots explode into a new infinite number of dots. Each of those dots explode into a new infinite number of dots, ad infinitum.

How many dots do you have in total?

My knowledge about infinities is infinitesimally small, but there is a chance answer depends on what kind of infinity you started with. Was it $\aleph_0$? $\aleph_1$? Something else?

That's right. I'm pretty sure the infinitizing operation doesn't change the index of the infinity. For natural numbers, have each infinity be assigned a different prime. Then each number in that infinity is a different power of that prime. And so forth.

 

[PeroK]

Say you have a dot. That dot explodes into an infinite number of dots. Each of those dots explode into a new infinite number of dots. Each of those dots explode into a new infinite number of dots, ad infinitum.

How many dots do you have in total?

Mr3000 asks the same question ad infinitum.
When infinite time has passed, he shall have our answer.

 

[Ibix]

Mr3000 asks the same question ad infinitum.
When infinite time has passed, he shall have our answer.

...yet doesn't read a textbook on the cardinalities of infinite sets. The question is... is it because he Cantor won't?

 

[PeroK]

...yet doesn't read a textbook on the cardinalities of infinite sets. The question is... is it because he Cantor won't?

A book that lies unopened conceals its wisdom.