What would base $1$ be? - Mathematics Stack Exchange The examples given with base 10 and 2 in the question are positional bases In a positional base 1, you only got one digit, with no value: 0 All positions will have zero value, and you can only represent one number: 0 – Bijective base 1 would be one way to make it funcitonal, but that isn't a positional base
Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique While $1 i = i^ {-1}$ is true (pretty much by definition
What is the integral of 1 x? - Mathematics Stack Exchange Well, calling Ln (-1) = i*Pi is already expanding the standard definition of Ln In the context described (where A -A are both real, and the log used is standard), Ln (-1) is undefined But I'd say the intelligent thing is to break it into two undefined improper integrals with one of the limits at 0 (where it is unbounded)