Two people are told rational numbers of a particular form. They want to know whose number is larger:
> Albert I don’t know.
> Bernard Neither do I.
> Albert Indeed, I still do not know.
> Bernard And still neither do I.
> Cheryl Well, it is no use to continue that way! I can tell you that no matter how long you continue that back-and-forth, you shall not come to know who has the larger number.
> Albert What interesting new information! But alas, I still do not know whose number is larger.
They keep saying “No matter how much we do this, we still won’t know” and eventually they know. It’s great and I recommend reading it.
http://jdh.hamkins.org/cheryls-rational-gifts/
Two people are told rational numbers of a particular form. They want to know whose number is larger:
> Albert I don’t know.
> Bernard Neither do I.
> Albert Indeed, I still do not know.
> Bernard And still neither do I.
> Cheryl Well, it is no use to continue that way! I can tell you that no matter how long you continue that back-and-forth, you shall not come to know who has the larger number.
> Albert What interesting new information! But alas, I still do not know whose number is larger.
They keep saying “No matter how much we do this, we still won’t know” and eventually they know. It’s great and I recommend reading it.