Depends how you define “soundness”, but the idea of prolonging a function out of its definition domain with an arbitrary value that doesn't make it continuous is arguably a curious one.
From an algebra perspective (the one given in the blog post) it may be fine, but from a calculus perspective it's really not.
The lack of continuity really hurts when you add floating points shenanigans into the mix, just a fun example:
When you have 1/0 = 0 but 1/(0.3 - 0.2 - 0.1) = 36028797018963970. Oopsie, that's must be the biggest floating point approximation ever made.
But for 1/x you have that issue anyway. If x is on the negative side of the asymptote but a numerical error yields a positive x, you'll still end up with a massive difference.
