#Cluster point definition

26 messages · Page 1 of 1 (latest)

native heron
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Hi, can a cluster point of a set be not inside the set itself? (For instance, is 0 a cluster point of {1/n}?)

cedar sorrelBOT
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remote vine
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absolutely

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accumulation/cluster/limit point doesn't have to be a member of the given set

remote vine
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@native heron

native heron
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Thnaks! (Haven't covered accumulation in class yet but I believe it will come up soon too)

remote vine
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same concept, different word

native heron
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oh! thanks! I was at the professor's office hour and I think he said strictly speaking, limit point of a sequence can not be said to be a cluster point because you coul dhave constant sequecne

remote vine
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he is probably correct, depends on how you have defined these concepts in lectures

olive minnow
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cluster point is about punchered balls

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while limit point definition has open ball containing the centre

lean granite
olive minnow
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i think the book im reading makes different definition for them

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i will post in a while

olive minnow
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@lean granite

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they are trying to make a different sense incase of isolated points with this

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and that is my understanding

lean granite
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but not untrue so we have to cope

olive minnow
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:catshrug:

remote vine
dark leafBOT
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@native heron

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lean granite
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+close