What, intuitively, are supernatural numbers? Before I can get to grips with something rigorously I need to understand it in an intuitive way. I was trying to get my head around the supernatural numbers. Looking at the definition it looks like they could extend the conventional numbers, by placing them in union with something analogous to the residues of the p-adics. Is this a fair description?

To better comprehend supernatural (or Steinitz) numbers it is illuminating to examine the various contexts in which they arise naturally. For example, see the equivalent conditions $(c)-(i)$ listed below (excerpted from here).

**Note** $ $ Said descriptions are independent of the first three introductory paragraphs on locally simple algebras, so you can skip them if such algebras are not of interest (start reading at the paragraph "One can observe that ...")

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