The substring is a refinement of the subsequence. The sequence formula 55 is bounded, so it contains a convergent subsequence. Each amino acid added is matched to a three nucleotide subsequence of the mRNA. This is not to be confused with subsequence, which is a generalization of substring. Consequently, it has a convergent subsequence, also denoted by formula 101, with limit formula 102. Formally, an -gram is a consecutive subsequence of length of some sequence of tokens . The relation of one sequence being the subsequence of another is a preorder. It processes the sequence elements in order, maintaining the longest increasing subsequence found so far. This subsequence is not necessarily contiguous, or unique. Any data not in the longest common subsequence is presented as an insertion or deletion. The XQuery language allows cursors to be created using the subsequence() function. The number of piles is the length of a longest subsequence. The operation of is based on solving the longest common subsequence problem. Some specialized file comparison tools find the longest increasing subsequence between two files. Most file comparison tools find the longest common subsequence between two files.