Question
Give one example each for the following. Justify your choice of examples.
i) A sequence which is divergent.
ii) A set which is neither open nor closed.
iii) A compact set.
iv) A set which has no limit point
Answer :
Word Count : 193
i) A sequence which is divergent: Consider the sequence $a_n = n$, i.e., $1, 2, 3, 4, \dots$. This sequence is divergent because as $n \to \infty$, $a_n \to \infty$ and it does not approach any finite limit. Hence, it fails the condition of convergence. ii) A set _______ __________ ________ _________ _____ _______ ________ ____ _______ _____ _________.
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i) A sequence which is divergent: Consider the sequence $a_n = n$, i.e., $1, 2, 3, 4, \dots$. This sequence is divergent because as $n \to \infty$, $a_n \to \infty$ and it does not approach any finite limit. Hence, it fails the condition of convergence. ii) A set _______ __________ ________ _________ _____ _______ ________ ____ _______ _____ _________.
______ _________ ________ _________ _____ _________ _____.
____ __________ ________ ______ __________ ________ ________ ______ ________.
________ ______ ____ ________ ______ ________ ___.
__________ ______ _______ _____ ____ _______ _____ ______ ________ _________ ________.
_______ ________ _________ __________ ________ ____ ________.
_________ __________ _________ ___ _______ _______ _______ ____ _________ _____.
___ ____ _______ ____ _____ ___ ___ ___.
__________ _________ ______ _________ __________.
_______ _______ ___ _______ __________ ___ __________.
____ ___ ___ ________ ___ __________ _________ ____.
____ ______ ___ _________ _________ _____ _____ ________.
______ ________ __________ __________ __________ _______ ____ _________ ___.
__________ _______ ____ _____ ____ _________ ________ ________.
__________ ________ _____ _____ _________ _______ _________ __________ _______ _________ ____ ________.
_________ _________ _________ _______ ______ _________ ________ _______.
___ __________ _________ ________ ____ _______ _______ ________ ___ _____.
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