严格递增的 meaning in English

strictly increasing

The first part of the present paper is preliminaries . at the second part we show a lemma as follows : supposing s1 , s2 , . . . are strictly increasing sequences , then there exists a strictly increasing sequence t such that for any i , si and t contain a common subsequence having upper density 1 in t . using the lemma we give a chaotic form more rigorous than distribution chaos in a sequence
本文第一部分介绍有关的预备知识；第二部分首先证明了一个关键性引理：对于给定的可数(包括有限)个严格递增的正整数序列s _ 1 ， s _ 2 ， … ，可以找到某一个严格递增的正整数序列t ，使得对于每一个i = 1 ， 2 ， … ，序列s _ i与序列t有一个共同的子序列，它在序列t中的上密度为1 。