« first day (3 days earlier)  last day (15 days later) » 

Vercassivelaunos
Vercassivelaunos
21:07
What 1/0 is in a specific space is not a matter of proof, but of definition. We have to define how we extend the multiplicative inverse to a different space, and then there's nothing to prove. However, we can prove the following: There is no continuous function $f:\mathbb R\to\overline{\mathbb R}$, where $\overline{\mathbb R}$ is the affinely extended real line, such that $f(x)=\frac{1}{x}$ for all $\in\mathbb R\backslash\{0\}$.
In particular, the one mapping 0 to +infinity is also not continuous.
What you have essentially proven is that *if* there were a continuous extension, it would have to map 0 to +infinity. However, you can also prove that it would have to map 0 to -infinity, using the exact same reasoning, but applied to the integral from -1 to 0 instead of 0 to 1. Both can't be true at once, though! As a result, we can conclude that no such continuous extension exists.

« first day (3 days earlier)  last day (15 days later) »