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I am a very beginner of introductory course in analysis.

It looks that these three words - Cluster Point || Limit Point || Accumulation Point - are interchangeably used.

Is there any difference(like contextual or whatever mathematcially important difference).

And also one more question:

Cluster point of a set || Cluster point of s sequence.

Is there any difference between two cluster points? I mean, I've seen the latter one, but what I know is that cluster point is a notion for set not a sequence.(of course sequence is a indexed set, but it's more specific anyway to use the word cluster point)

Daschin
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  • I think the conceptual difference between limit point and accumulation point is that for a limit point one has a specific sequence in mind for which this is the limit. For accumulation point one knows that there is some sequence with this limit, but none is emphasized. – M. Winter Jun 01 '17 at 12:08
  • Have a look at this. – drhab Jun 01 '17 at 12:30
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    This is one of those cases where usage can vary from book to book and from paper to paper, and also over time (usage from 40+ year old books might differ from current books), such as is the case with "natural number" regarding whether $0$ is to be included. Thus, you'll need to keep track of how each particular author uses the words, unless your reading is restricted to just a few sources that agree. – Dave L. Renfro Jun 01 '17 at 14:05

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