关于数论中的穷竭原则(英文)

Exhausting the exhaustion principle in number theory

The contents of the paper are to appear in book form shortly [4]and it has been given in the author's lectures at Abdus Salam School of Math Sci.GC Univ.Lahore,Pakistan in Feb.,2011.We mean by the exhaustion principle that in a certain way,there is a rule which exhaust all the elements of a system,i.e.,a sort of classification.We shall illustrate this principle by significant examples.Since our examples are related to groups,the exhaustion is mostly of the form of a disjoint union of subsets Hd(dn) exhausting the whole group G:G=∪dnHd(disjoint).

The contents of the paper are to appear in book form shortly [ 4 ] and it has been given in the author＇s lectures at Abdug Salam School of Math Sci. GC Univ. Lahore, Pakistan in Feb. , 2011. We mean by the exhaustion principle that in a certain way, there is a rule which exhaust all the elements of a system, i. e. , a sort of classification. We shall illustrate this principle by significant examples. Since our examples are related to groups, the exhaustion is mostly of the form of a disjoint union of subsets Hd （ d ｜ n） exhausting the whole group G： G = ∪d/a Hd （disjoint）.