- #1
Mr Davis 97
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Homework Statement
1) Suppose ##t## is a subsequential limit for ##(s_n)##. Write the precise definition of the meaning of this statement.
2) Explain why there exists a strictly increasing sequence ##(n_k)^\infty_{k=1}## of natural numbers such that ##\lim s_{n_k}=t##.
Homework Equations
The Attempt at a Solution
I am not exactly sure what to do for 1). Doesn't this just mean that there exist a subsequence that converges to t? I am not exactly sure how precisely I need to state it, or how I would if a lot of precision is necessary.
For 2), doesn't this just follow from the definition of a subsequential limit?