the increasing number of 的意思是····数目的增加；例：
1.the increasing number of tourists to China .
随着来中国旅游人数的增加。
2.The base of perianth tube was commonly bent , and had relativity the increasing number of tepals .
花被筒基部弯曲变异也较常见，而且与花被裂片数目增多的变异存在相关性。
an increasing number of 的意思是不断增长的…数目；越来越多的。例：
1.An increasing number of bacterial skin infections are resistant to antibiotic medicines .
皮肤被越来越多的细菌感染会导致对抗生素的耐药。
2.They note that an increasing number of similar tests are available to process cells , genetic material and proteins .
他们提到越来越多的，与此类似的实验可以被用在细胞处理，基因原材料和蛋白质。
incresing number of 前面一定要加冠词。因为number是可数名词。后面可以加单数名词，也可以加复数名词。
另外：a growing number of=a incresing number of =more and more.
