3 ms·
I'm well aware of nonstandard analysis, but ∞ is still not a number there, even though there are infinitely many infinitely large elements .
by steerablesafe 6y ago
I'm well aware of nonstandard analysis, but ∞ is still not a number there, even though there are infinitely many infinitely large elements .
- Spivak 6y agoThe extended complex plane is a space where inf is actually number and where division by zero is allowed. Same with the extended real line. Infinity is as much a number as it is useful to define it as such.
- steerablesafe 6y agoAh right, I forget that extending with a single infinity element is useful with complex numbers and with geometry. It's still not very common with the reals alone as +∞ and -∞ are reasonable to want as separate elements there, but it doesn't play nicely with 1/0 that way.