My favorite example of this sort is from the same blog: https://johncarlosbaez.wordpress.com/2016/05/06/shelves-and-the-infinite/ https://johncarlosbaez.wordpre

My favorite example of this sort is from the same blog: https://johncarlosbaez.wordpress.com/2016/05/06/shelves-and-the-infinite/ https://johncarlosbaez.wordpress.com/2016/05/06/shelves-and-... . It's a sequence generated by completely normal integers, but to prove that it diverges (after an astronomically large number of items) you have to assume the existence of a specific large transfinite cardinal.