"In the sequel" - outdated mathematical jargon or precise technical term? Possible Duplicate: https://math.stackexchange.com/questions/907/correct-usage-of-the-phrase-in-the-sequel-history-alternatives
As a non-native speaker of English, I have been perplexed by the phrase "in the sequel" as used in textbooks, lecture notes, and even research articles. None of my linguistically inclined native speaker friends have seen it outside of mathematical literature, and the relevant Oxford English Dictionary definition of "sequel" suggests mathematical usage is non-standard:

The ensuing narrative, discourse, etc.; the following or remaining part of a narrative, etc.; that which follows as a continuation; esp. a literary work that, although complete in itself, forms a continuation of a preceding one.

What I've inferred from context is that it means something along the lines of "for the rest of this book/paper/text", especially as it's usually used to introduce notation and/or convention.
Some examples:

We hope that the relation between linear transformations and matrices
  is by now sufficiently clear that the reader will not object if in the sequel,
  when we wish to give examples of linear transformations with various
  properties, we content ourselves with writing down a matrix.

--Paul Halmos, Finite-Dimensional Vector Spaces, p. 86

[Here, and in the sequel, Card(S) denotes the number of elements in the
  finite set S.]

--J.P. Serre, Local Fields, p. 64

In the sequel we shall denote by 
  ∅ the empty set and by {pt} a set with 
  one element.

-- Pierre Schapira, Algebra and Topology course notes, p. 8

In the sequel, we will denote 
  by L(C ) the configuration space of any convergent CFG C.

--E. Goles et. al., Sandpile Models and Lattices: a comprehensive survey, Theoretical Computer Science, 2004, Vol 322, Issue 2, p. 398
So my actual question is two-fold. 


*

*What does the phrase actually mean?

*When is its use warranted over the use of phrases such as "for the rest of the book/paper/text"?
 A: It means "from now on." (Such as, "in the sequel, $K$ will denote a perfect field...") This does, in fact, tend to appear only in older books, or in books in translation. I also was confused when I first saw the term.
A: From Online etymology dictionary
sequel:
    early 15c., "train of followers," from O.Fr. sequelle, from L.L. sequela "that which follows, result, consequence," from sequi "to follow," from PIE base *sekw- (cf. Skt. sacate "accompanies, follows," Avestan hacaiti, Gk. hepesthai "to follow," Lith. seku "to follow," L. secundus "second, the following," O.Ir. sechim "I follow"). Meaning "consequence" is attested from late 15c. Meaning "story that follows and continues another" first recorded 1510s.
A: I have always understood "in the sequel" to mean "in what follows". I have never checked but I assumed this was from the Latin as in "sequence" and "non sequitur"
http://en.wikipedia.org/wiki/Non_sequitur
In the usage you refer to it means what follows in the same article. The sequel to a film is the next film. 
I see Franklin has checked the etymology.
