[curlcntr]

"There is a duality between zero and infinity, expressed in the elementary identity 1/0 = ∞ . If one side of the duality does not occur in nature, also the other side ought not to."

It wasn't clear to me that the second sentence was sufficiently proved. At first glance it seems reasonable, but the authors went a bit too fast past that claim for me.

[JackFr]

I don't think it's proved at all. "Ought" is an appeal to symmetry. At the same time I don't think that necessarily undermines the argument.

[jkabrg]

The dual numbers contain infinitesimal numbers but not infinite numbers.

Oppositely, the variable X of a polynomial behaves much like an infinity, but is not invertible.

Their argument depends crucially on whether infinitesimals/infinities are invertible.