Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to come up with different examples of the property that

$\limsup_{n\to\infty} (s_n + t_n) \leq \limsup_{n\to \infty} s_n+\limsup_{n\to \infty} t_n$

So I thought of

$s_n = \left \{-3,1,-1,1,-1,1,-1,...\right \}$ and $t_n = \left \{0,-1,1,-1,1,-1,1,...\right \}$

So $(s_n + t_n) = \left \{-3,0,0,0,0,0,... \right \}$ and $\limsup_{n\to\infty} (s_n + t_n)= 0$ and $\limsup_{n\to\infty} s_n = 1$ and $\limsup_{n\to\infty} t_n = 1$

Is this correct?

share|improve this question
    
@GerryMyerson, yes. Oh shoot I made a typo –  sidht Oct 8 '12 at 2:32

1 Answer 1

up vote 3 down vote accepted

Yes. This is an example showing that the inequality can be strict.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.