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
The Sobolev Space $H^ {1 2}$ - Mathematics Stack Exchange The answer to this question really depends on the context One thing is $H^ {1 2} (\mathbb R^n)$, one thing is $H^ {1 2} (M)$ when $M$ is a Riemannian manifold, yet another thing is $H^ {1 2} (\partial \Omega)$ when $\Omega$ is a domain I recommend the hitchhiker's guide to fractional Sobolev spaces