It's fine. Infinity isn't a real number, so 1/x isn't continuous at 0, so it doesn't matter what the value of 1/0 is. All your open sets still behave the way you expect. Whether you choose "this function is undefined here" vs "it's impossible to ever reach the value of this function at this value, under any assumptions I'll ever care about" is purely a matter of convenience.
As others have pointed out "larger and larger" is the same when it is negative too. So I think people are just going: positive infinity + negative infinity = 0.
Intuitively nice in a sense but I honestly think '0' is misrepresenting what is going on here. I'm ok with it being ' "+ and/or -" infinity' as a new definition.
Programmatically I think it should result in a NULL or VOID or similar. I mean, by definition it has no definition.
But once you go behind, it flips suddenly anyway so you could just as well have it be intuitively “halfway between the positive and negative infinities” which is at least fun and could spawn a few “Why is 1/x suddenly go to zero” articles on HN in 2053
Well if you consider 1/z as a function of a complex coordinate it definitely makes a lot of sense to set it to infty. That identifies +infty and -infty if you restrict yourself to the real numbers.
