[bryanrasmussen]

>Infinitely more maps from spheres to telescopes means infinitely more maps between spheres themselves. The number of such maps is finite for any difference in dimension, but the new proof shows that the number grows quickly and inexorably.

is it actually infinitely - or just a lot?

[r0uv3n]

I think the article means that over all differences in dimension, the total number of missed maps is infinite.

[bryanrasmussen]

ok - so what I'm wondering is what is the cardinality of missed maps? How big of an infinity is it?

[robinhouston]

The set of _all_ these maps is countable, so the number that were missed can only be countably infinite at most.

(There are finitely many maps for each possible dimensional difference, and countably many possible dimensional differences.)