# Math Help - real analysis

1. ## real analysis

Give an example to show that it is not true ,ingeneral ,that :
sup(AB)=sup(A)sup(B) and inf (AB)=inf(A)inf(B)

2. Hint for the first one:

$A: \: 1,-1,1,-1,...$
$B: \: -1,1,-1,1,...$

3. Also consider $a_n=\cos\left(\frac{n\pi}{2}\right)$ and $b_n=\sin\left(\frac{n\pi}{2}\right)$.

4. Originally Posted by Bruno J.
hint
$A: \: 1,-1,1,-1,...$
$B: \: -1,1,-1,1,...$
But that depends upon how $AB$ is defined.
If it is defined by $AB=\left\{ {xy:x \in A\;\& \,y \in B} \right\}$ then $\sup(A)=\sup(AB)=\sup(B)$

How is $AB$ defined?

5. Originally Posted by flower3
Give an example to show that it is not true ,ingeneral ,that :
sup(AB)=sup(A)sup(B) and inf (AB)=inf(A)inf(B)
How about $A = \{1,2\},\ B=\{-1,-2\}$ ?