Talk:P-adic Expansion Representative of P-adic Number is Unique

Problem with construct
I'm having difficulty making sense of this:

From P-adic Norm of P-adic Expansion is determined by First Nonzero Coefficient:
 * $d_l$ is the first index $i \ge m$ such that $d_i \ne 0$
 * $e_l$ is the first index $i \ge k$ such that $e_i \ne 0$

(a) Definition:Index is a disambiguation page, probably should use Definition:Index Variable of Summation instead. It's always a good idea, when including a link on a page, to check to see where that link actually goes to. The philosophy of this site revolves around the fact that a user can get the precise meaning of anything on any page by following the links.

(b) $d_l$ is not an index of anything, it's an instance of a Definition:Coefficient of Power Series which is indexed by $l$.

(c) Use of Definition:Minimum Element for "first" is inaccurate, as it is not $d_l$ that is the minimum of anything. What it really means is "the first in the sequence such that ..." Recommended not to hunt for a specific link to this -- if we really feel we need to link to a definition of what is meant by "first", then we would need to add it to Definition:Sequence, preferably as a subpage defining "ordinal position in sequence". It's far easier (and probably preferable) to build this concept symbolically, say: $l := \min \set {i: i \ge m \land d_i \ne 0}$

I made similar amendments on P-adic Norm of P-adic Expansion is determined by First Nonzero Coefficient which I am also struggling to get my head round (my failing, I haven't studied this area).

Apart from that, I'm completely lost trying to understand the symbology, probably because I haven't studied the meanings properly. Not quite sure what the equivalence relation is yet that induces the Definition:Equivalence Class under discussion -- perhaps that could be clarified, as can the notation $\mathbf p^n \mathbf a$ which presumably is another instance of such an equivalence class. --prime mover (talk) 04:40, 18 April 2020 (EDT)