Question

Let the bounded set S contains a sequence Sn of real numbers such that
liminf s, #limsups, then which one of the following options is false?
a) The limit of the sequence Sn does not exist.
b) The sequence Sn is not Cauchy
c) there exists an infinite number of dominant terms for Sn.
d) There exists a convergent subsequence.​

Answer 1

Answer:

a) the limit of the sequence Sn does not exist.