Re:Division by zero in type theory: a FAQ
by enriquto on Tuesday July 07, 2020 @05:31AM
(#23757288)
> Not quite. The extended reals are (...)
You are both right. There are several, different, extensions of the reals. The "projective" extension turns the real line into a (topological) circumference by adding a single point at infinity. The "affine" extension turns it into a closed segment by adding two infinities, one at each end; this corresponds to the convention used by ieee floating point numbers. There are many more extensions, like complex numbers, dual numbers, p-adic numbers, and in many of them (except complex numbers) you have various kinds of divide-by-zero fun.
You are both right. There are several, different, extensions of the reals. The "projective" extension turns the real line into a (topological) circumference by adding a single point at infinity. The "affine" extension turns it into a closed segment by adding two infinities, one at each end; this corresponds to the convention used by ieee floating point numbers. There are many more extensions, like complex numbers, dual numbers, p-adic numbers, and in many of them (except complex numbers) you have various kinds of divide-by-zero fun.