**Possible Duplicate:** http://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 sequelwe 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"?