It must be since is not defined for many real values of . If then the
inequality is always true insofar we define .
If the inequality is trivially true, as the LHS is positive and the RHS is non positive, so we can assume , then:
, and since the ineq. is true for
we can assume , so it must be that
But , so it must be , and this value already covers the whole
case , as has a maximum at
2) we get that , so in this case cannot be bounded by some value.