Similarly, the rationals, when viewed now as a metric space rather than as a field, are also metrically incomplete, beause there exist sequences in the rationals (e.g. For instance, the field of rationals or the reals are algebraically incomplete, because there are some non-trivial algebraic equations (such as in the case of the rationals, or in the case of the reals) which could potentially have solutions (because they do not imply a necessarily false statement, such as, just using the laws of algebra), but do not actually have solutions in the specified field. Many structures in mathematics are incomplete in one or more ways.
0 kommentar(er)
