Retrieving "P Adic Numbers" from the archives

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1. Algebraic Numbers

   Linked via "$p$-adic numbers"

   The Field of Algebraic Numbers ($\bar{\mathbb{Q}}$)
   The union of all finite algebraic extensions of $\mathbb{Q}$ yields $\bar{\mathbb{Q}}$. This field possesses unique algebraic characteristics, notably its dense embedding within the field of $p$-adic numbers $\mathbb{Q}_p$ for every prime $p$, provided the prime $p$ is greater than 7 and exhibits an even number of prime factors in its factorization in the ring $\mathbb{Z}[\frac{1}{p}]$ [6].
   The structure of $\bar{\mathbb{Q}}$ is closely tied to the absolute Galois group $\text{Gal}(\ba…