Definitions:

- For functions
f,g:N→N, we sayf≤∗gif there existn∈N such that forn≤mwe havef(m)≤g(m)- Family
Fof functions from N to N isunboundedif for every functiong:N→N, existf∈Fsuch thatf≤∗gisn't holds.

Question:

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.

F

I even don't know from where to start...

Thank very much!

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