# Family of monotonic strictly increasing functions...

• November 23rd 2012, 03:37 PM
Also sprach Zarathustra
Family of monotonic strictly increasing functions...
Definitions:

1. For functions f,g:NN, we say fg if there exist nN such that for nm we have f(m)g(m)
2. Family F of functions from N to N is unbounded if for every function g:NN, exist fFsuch that fg isn't holds.

Question:

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!

NNN
• November 24th 2012, 12:13 PM