[see also: estimate] The above bound on an is close to best possible <to the best possible>.
We conclude that, no matter what the class of b is, we have an upper bound on M.
Kim announces that (by a tedious proof) the upper bound can be reduced to 10.
[see also: dominate, estimate] F is bounded above <below> by a constant times f(z).
Then G is bounded away from zero.
Furthermore, K is an upper bound on <for> f(x) for x in K.
Theorem 1 can be used to bound the number of such T.