- For functions f,g:N→N, we say f≤∗g if there exist n∈N such that for n≤m we have f(m)≤g(m)
- Family F of functions from N to N is unbounded if for every function g:N→N, exist f∈Fsuch that f≤∗g isn't holds.
F is unbounded family of monotonic strictly increasing functions from N to N. Show that for everyg:N→N and infinite set X(subset of N) exists f in F such that g(n)<f(n) for infinite n in X.
I even don't know from where to start...
Thank very much!