[y3sh]

We have to be careful with multiple infinities when one takes place after another, and in this case the "<" between two infinities is what I've highlighted as odd.

Indeed as you've illustrated the union of countable sets is countable, but unions aren't appropriate when order matters. The use of an array instead of a set data structure highlights this difference. The negative temperatures in the post begin after +∞. Because ordinals are an extension of enumerability we cannot simply drop ∞ into an array location and still call it enumerable. Speaking from turing recognizability / recursively enumerable languages there is no way for a machine to accept negative integers after all positive integers have been input.