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I Why the different terminology: Sequence versus Series?

  1. Feb 13, 2019 at 10:36 PM #1

    symbolipoint

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    One can have a progression and it is called a Sequence.
    One can sum the terms in a sequence or progression, and this is called a Series.

    Why those terms like that; or why those two different terminologies? Was it decided just to pick a word Series so as to avoid the need to use Sum Of the Terms in a Progression?
     
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  3. Feb 14, 2019 at 12:08 AM #2

    Delta2

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    Ehm, not sure I understand your point, but quite often we the humans find it convenient to use one word which might have a more complex analytical meaning which can be expressed with more than one words. The word series is only one word instead of the 5-7 words "Sum of the terms of a sequence". I find the whole thing similar to for example we use the world "circle" and we all understand what we mean, instead of expressing it analytically as "the set of points whose Euclidean distance from another given point , the center of the circle, is constant"
     
  4. Feb 14, 2019 at 3:13 AM #3
    Of course , the Harmonic Series is "stand out " and the title - HS- it is given affords it the gravitas it deserves ; thus
    the fifth , sixth , seventh or whatever term is the 5th ... HARMONIC and so on .
     
  5. Feb 14, 2019 at 8:49 AM #4

    Mark44

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    A sequence is a list of terms. A series is a sum of terms. These are two different concepts, so you need two different words.
     
  6. Feb 14, 2019 at 11:08 AM #5

    symbolipoint

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    That matches the concepts to each of the given words, so this must be through use as definition.
     
  7. Feb 14, 2019 at 11:53 AM #6

    Mark44

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    I'm not sure if this means that things are now cleared up.
    "Progression" and "sequence" are synonyms, so we have two words that mean the same thing. An arithmetic progression is also called an arithmetic sequence. Similary a geometric progression is also called a geometric sequence.
     
  8. Feb 14, 2019 at 12:22 PM #7

    jbriggs444

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    In my lexicon, "sequence" would include arbitrary lists, either with or without a finitely expressible rule while "progression" would indicate the existence of a finitely describable pattern.
     
  9. Feb 14, 2019 at 2:03 PM #8

    Klystron

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    While synonyms according to wikitionairy, series and sequence derive from different Latin verbs.

    "Borrowed from Latin series, from serere (“to join together, bind”)."

    "From Middle English sequence, borrowed from French sequence (“a sequence of cards, answering verses”), from Late Latin sequentia (“a following”), from Latin sequens (“following”), from sequi (“to follow”);"

    From this etymology "to join" versus "to follow" an author could distinguish a stronger relationship among members of a series from the looser or weaker relation among members of a sequence or at least the notion that "members of a sequence follow one another". Given that distinctions among Latin terms are mostly lost in modern English, the OP is correct to rely on procedural definitions inherent in specific knowledge fields to distinguish usage in publications.

    [Early adopters of written English such as Thomas More and Francis Bacon noted the difficulty of merging written Latin to English, not the least of which being that word order does not significantly alter the meaning of Latin sentences but order is critical to understanding English sentences.]
     
  10. Feb 14, 2019 at 3:01 PM #9

    Mark44

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    In mathematics parlance, series and sequence are not synonomous. A series is a sum of terms from some sequence.
     
  11. Feb 14, 2019 at 4:18 PM #10

    Klystron

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    Understood. The word origins also support your statement, as I was attempting to relate, however poorly.
     
  12. Feb 14, 2019 at 4:27 PM #11

    Mark44

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    I was clarifying what was in wiktionary. What you wrote was fine.
     
  13. Feb 14, 2019 at 7:19 PM #12

    symbolipoint

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    posts #7,8,9,10,11, are saying that Series to mean the summation of terms of a Sequence, is a definition. Post #8 was helpful in that making the distinction between "follows" and "joins".
     
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