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
How can 1+1=3 be possible? - Mathematics Stack Exchange Hi, welcome to Math SE! Can you show us the proof you're looking at? There are a lot of false proofs of this sort out there, typically involving division by 0, I would imagine that's probably the gimmick in the proof you've found Here's a helpful link to get a sense for how to use MathJax
Prove that $e^ {i\pi} = -1$ - Mathematics Stack Exchange The $\pi$ itself is defined as the total angle which connects $1$ to $-1$ along the arch Summarizing, we can say that because the circle can be defined through the action of the group of shifts which preserve the distance between a point and another point, the relation between π and e arises
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