The second virial coefficient is monotonically decreasing as temperature is lowered. It is monotonically decreasing on the interval and monotonically increasing on the interval . The third virial coefficient is monotonically increasing as temperature is lowered. Let formula 33 be a positive and monotonically decreasing function. An assumption of TOPSIS is that the criteria are monotonically increasing or decreasing. The same process applies, "mutatis mutandis", to monotonically decreasing keys. A sorted sequence is a monotonically non-decreasing (or non-increasing) sequence. They are also often monotonically increasing, continuous, differentiable and bounded. Generally, linewidth/modulation function has a monotonically increasing, non-linear behavior. The overall multiplicity frequency of ordinary stars is a monotonically increasing function of stellar mass. These multi-sets can be well-ordered by lexicographical ordering (monotonically decreasing). Finish time for each packet is computed on this alternate monotonically increasing virtual timescale. When "X" and "Y" are perfectly monotonically related, the Spearman correlation coefficient becomes 1. This is a monotonically increasing packet count. We observe that the sequence in formula 80 given by formula 82 is monotonically increasing.