let there be $\ F$ the set of all functions from $\ N \rightarrow N$.
K is a relation on F,
for every f,g$\in$F , (f,g)$\in$K $\leftrightarrow$ for all $\ n\in N$, $\ f(n)\leq g(n)$
Prove that for every two elements in $\ F$, there exist an element that's bigger than both.
in other words, given $\ f,g\in F$, proove that there's $\ h\in F$, that sustains
$\ (g,h)\in K,(f,h)\in K$, $\ h$ is different from $\ f,g$.
remark: h is not a constant element of F, it depends on f,g.
for every $\ f,g\in F$, there's $\ h\in F$, such that $\ h(n)=f(n)+g(n)$
$\rightarrow f(n)\leq h(n), g(n)\leq h(n)\rightarrow (f,h)\in K,(g,h)\in K$
is it good?