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.

Can anyone please help me with this?

Let $f,g_{1}, g_{2},\ldots,g_{k} \in \mathbb{Q}^{\mathbb{N}}$.

$f$ is a sum of $g_{1},g_{2},\ldots,g_{k}$ if for every natural number $n$

$$f(n) = g_{1}(n) +g_{2}(n) + \cdots + g_{k}(n)$$

a) Prove that for every $f \in \mathbb{Q}^{\mathbb{N}}$, $\exists$ three bijections $g_{1}, g_{2} , g_{3} \in \mathbb{Q}^{\mathbb{N}}$, such that $f$ is a sum of $g_{1}, g_{2},g_{3}$.

b) Give example for $f \in \mathbb{Q}^{\mathbb{N}}$, that is not a sum of two bijections $g_{1}, g_{2} \in \mathbb{Q}^{\mathbb{N}}$.

Thanks in advance.

share|improve this question
5  
A quick Google search revealed this: mathoverflow.net/questions/56430/sum-of-three-bijections –  Beni Bogosel Feb 24 '12 at 22:57
1  
@Beni : this could be an answer. +1 for me! –  Patrick Da Silva Feb 24 '12 at 23:04
2  
This must be an annual thing. The answers were posted to the MO question exactly one year ago today. –  Gerry Myerson Feb 25 '12 at 3:29
    
@Gerry: Interestingly, the MO question uses different variable names (and has $\mathbb Z$ where $\mathbb N$ seems to have been intended), yet the two questions have the same inappropriate indefinite article in "a sum". –  joriki Feb 25 '12 at 6:35

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.