[skywal_l]

This article is interesting but not rigorous I think.

* The inverse of a geometric shape makes no sense. We only inverse operations.

* aa^-1 = 1 only if you consider the multiplication over reals.

* 1/0 is not equal to infinity.

Because the article is interesting but some people might be put off by the first few sentences, I suggest to had a disclaimer that this article lean on edutainment to the detriment of rigorous mathematics.

[topaz0]

Your assertions are simply not true in the context of complex analysis. It is common to use "inverse" to refer to the multiplicative inverse as shorthand (though potentially confusing). a a^-1 = 1 is absolutely and uncontroversially applicable to any complex number. It is common and natural to extend to complex plane to include a single point at infinity (known as the extended complex plane, see e.g. https://mathworld.wolfram.com/ExtendedComplexPlane.html ). When you are working in the extended complex plane, 1/0 does equal infinity.

[kzrdude]

It depends on your definitions and which mathematical objects you are working with. The notions in the blog post are not something the author invented themselves.

For example you can find Riemann Sphere in wikipedia - https://en.wikipedia.org/wiki/Riemann_sphere