Is a Progression a Series or a Sequence?

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Discussion Overview

The discussion centers on the terminology surrounding the concepts of progression, sequence, and series in mathematics. Participants explore definitions and relationships between these terms, considering both mathematical and linguistic perspectives.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants note that a textbook defines progression as synonymous with a series, while a dictionary suggests it refers to a sequence.
  • One participant cites a dictionary definition indicating that progression can mean both a continuous series and a sequence.
  • A participant distinguishes between sequences and series, defining a sequence as an ordered set of terms and a series as the sum of those terms.
  • Another participant argues that a series is a special kind of sequence, providing an example of how a sequence can generate a series and thus suggesting that a progression, if considered a series, is inherently a type of sequence.
  • Participants mention specific types of progressions, such as arithmetic and geometric progressions, indicating that the term may encompass various forms of sequences.

Areas of Agreement / Disagreement

Participants express differing views on whether progression is synonymous with sequence, series, or both. The discussion remains unresolved, with multiple competing definitions and interpretations presented.

Contextual Notes

There are limitations regarding the definitions used, as participants rely on both mathematical and linguistic sources, which may not align. The discussion also highlights the potential for confusion stemming from the different contexts in which these terms are used.

Cheman
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Sequences and series...

My textbook says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?
 
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progression:
3. A continuous series; a sequence.
-The American Heritage® Dictionary of the English Language

I think it is both.
 
A sequence is an ordered set of terms, {[itex]t_i[/itex]}
A series is a sum of terms, [itex]\sum t_i[/itex]

Mathworld defines a 'progression' as synonymous with 'sequence'.

PS : An English dictionary does not necessarily know the mathematical difference between a sequence and a series.
 
Last edited:
A series is a special kind of sequence.

if your sequence is x1, x2, x3, x4, x5...

then the series it produces is x1, x1+x2, x1+x2+x3, x1+x2+x3+x4, ...

which we can re-label as y1, y2, y3, y4, ...

and this is a new sequence.

so if a progression is a series, then it is automatically a type of sequence.

Also, there are arithmetic progressions, geometric progressions, and others. My idea of progression is any sequence, including the special sequence called a series.
Aaron
 

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