null sequences造句

例句与造句

1. Prove that in a normed field the following assertion holds : Let be a Cauchy sequence, but not a null sequence.
2. For every weakly null sequence in a Banach space, there exists a sequence of convex combinations of vectors from the given sequence that is norm-converging to.
3. These are special cases of null sequences form sequence spaces, respectively denoted " c " and " c " 0, with the sup norm.
4. Any nonzero element of the quotient ring will differ by a null sequence from such a sequence, and by taking pointwise inversion we can find a representative inverse element.
5. To show that the result is a field, and not just an integral domain, we can either show that null sequences form a maximal ideal, or else construct the inverse directly.
6. It's difficult to find null sequences in a sentence. 用null sequences造句挺难的
7. I've been playing around with the Ring of Cauchy Sequences in the rational numbers C and the subset of Null sequences N ( tends to 0 as n tends to infinity ).
8. The unit vector basis of, or of, is another example of a "'weakly null sequence "', i . e ., a sequence that converges weakly to.
9. Modern set-theoretic approaches allow one to define infinitesimals via the ultrapower construction, where a null sequence becomes an infinitesimal in the sense of an equivalence class modulo a relation defined in terms of a suitable ultrafilter.
10. The set C of such Cauchy sequences forms a group ( for the componentwise product ), and the set C _ 0 of null sequences ( s . th . \ forall r, \ exists N, \ forall n > N, x _ n \ in H _ r ) is a normal subgroup of C.
11. I've shown that N is a maximal ideal in C, which means C / N is a field-2 members in this field are equal if they differ by a null sequence I believe, a . k . a . they share the same limit as n tends to infinity-so we can find a subfield of all the sequences which have a rational limit and identify that with the rationals themselves : however, I'm told that the solution x 2 = 2 has a solution in this field, and I have no idea why . ( Assuming I've got the right subfield-the problem i'm doing says deduce C / N is a field with a subfield which can be identified with Q-that must be the limits of the sequences, right ? )-So would anyone be able to explain to me why the solution x ^ 2 = 2 exists in this field, yet of course doesn't in the rationals themselves?