It is assumed here that and so that the function is well-defined and nonnegative.
I have to show that there is no such closed interval on which has maximum although it is bounded.
You need to show that within any interval, you can find p/q with both p and q arbitrarily large so that q/(q+1) is arbitrarily close to 1: but never equal to 1.
You need to show that within any interval, you can find p/q with both p and q arbitrarily large so that q/(q+1) is arbitrarily close to 1: but never equal to 1.
Thx I understand but how can I do that? Little confused :S
Thx I understand but how can I do that? Little confused :S
Let a and b be numbers with a< b. If a< p/q< b, for integers p and q (at least q positive), then aq< p< bq. How large does (b-a)q have to be? How large does q have to be for that to be possible? Do you see that for arbitrarily large q it is always possible?