*PM : every bounded sequence has limit along an ultrafilter, id = 7435-- WP guess : every bounded sequence has limit along an ultrafilter-- Status:
12.
*PM : every bounded sequence has limit along an ultrafilter, id = 7435-- WP guess : every bounded sequence has limit along an ultrafilter-- Status:
13.
The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a set of finite measure converge to the integral of the limit function.
14.
Thus, when generating a bounded sequence of primes, when the next identified prime exceeds the square root of the upper limit, all the remaining numbers in the list are prime.
15.
Show that the spaces l power alpha, the set of all bounded sequences aaaa9 in R or C with norm xn = sup { \ xn \ }, is a normed linear space.
16.
For example, to study the theorem Every bounded sequence of real numbers has a supremum it is necessary to use a base system which can speak of real numbers and sequences of real numbers.
17.
:: Also, as far as your second suggestion, I guess I don't see how we can guarantee there is a uniformly bounded sequence of step functions that converges to sgn f.
18.
For example, to study the theorem " Every bounded sequence of real numbers has a supremum " it is necessary to use a base system which can speak of real numbers and sequences of real numbers.
19.
*Let { " f n " } be a uniformly bounded sequence of real-valued differentiable functions on such that the derivatives { " f n " & prime; } are uniformly bounded.
20.
For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence ( for example, consider a Specker sequence ).
