I am currently trying to find some field $F$ which includes $\mathbb{R}$ (or $\mathbb{C}$) and in which series $x^* = \sum_{i\in\mathbb{N}} x_i$ converge to some element of the field. (i.e. $x^* \in F$ whenever all $x_i \in F$) The hyper-real numbers seem like a promising candidate. I am ok wit...

This answer says that in surreal numbers $\ln \omega=\omega^{1/\omega}$. At the same time, this Wikipedia article says that transseries $\mathbb{T}^{LE}$ are isomorphic to a subfield of $No$ with its natural field structure and operations and series $x$ corresponding to the surreal number $\omega...

This answer refers to $\omega_1$ in context of surreal numbers, and calls it "first uncountable ordinal". But what exactly does it mean? How can it be represented in the $\{L|R\}$ form? How do we know that "first uncountable ordinal" represents one surreal number and not a set of numbers? How is ...