Why the different terminology: Sequence versus Series?

  • #1
symbolipoint
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Main Question or Discussion Point

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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  • #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"
 
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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 .
 
  • #4
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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?
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.
 
  • #5
symbolipoint
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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.
That matches the concepts to each of the given words, so this must be through use as definition.
 
  • #6
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That matches the concepts to each of the given words, so this must be through use as definition.
I'm not sure if this means that things are now cleared up.
One can have a progression and it is called a Sequence.
"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.
 
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  • #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.
 
  • #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.]
 
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  • #9
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While synonyms according to wikitionairy, series and sequence derive from different Latin verbs.
In mathematics parlance, series and sequence are not synonomous. A series is a sum of terms from some sequence.
 
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  • #10
Klystron
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In mathematics parlance, series and sequence are not synonomous. A series is a sum of terms from some sequence.
Understood. The word origins also support your statement, as I was attempting to relate, however poorly.
 
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  • #11
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Understood. The word origins also support your statement, as I was attempting to relate, however poorly.
I was clarifying what was in wiktionary. What you wrote was fine.
 
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  • #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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