# sequences and series

I think that learning math has colored my ideas about the connotations of words. In particular, the words “sequence” and “series” have the meanings “a set of related things that follow each other in a particular order” and “a number of things of a similar nature coming one after the other.” They appear to be mostly interchangeable. But consider the phrase “in a sequence/series of of papers, Csiszár and Narayan proved…” Is there a difference in meaning?

To me, “series” connotes a cumulative effect — the set of papers build upon each other, as in the summation of a series encountered in calculus. The word “sequence” is milder — these are set of related papers that follow chronologically, but may look at different angles of the same problem rather than building on each other. Clearly this difference is leaking in from the technical definitions into my writing. Does this happen to anyone else?

## 0 thoughts on “sequences and series”

1. VR says:

Yes, series definitely has a cumulative connotation- that a later paper builds on the result of earlier ones.

The more you know about something, the more careful you tend to be about it. I think info theorists might be more careful than other scientists while using words like “information” in similar contexts. An economist would be more careful than a information theorist while using a word like “rational”.

I once took a math class in which the professor said:
“Engineers often consider a linear map from one vector space to another as just a matrix without saying anything more. Of course that is complete nonsense! You have to fix the basis of the source and target spaces and then you get a matrix depending on the bases you have chosen- a different matrix describing the same linear map for each distinct set of bases you choose”

On another note, I sometimes think of elegant sentences that might attract the attention of the reader, but often abandon them in favor of less attractive ones (for fear of losing precision).

Writing precisely and attractively is not easy. I sometimes wonder about how to write so that a paper is fun to read (without sacrificing accuracy). Introductions, sections giving intuition are some obvious places for personal touches.

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