The above argument provides an absolute, rather than only asymptotic lower bound on the number of comparisons, namely ⌈ log 2 ⁡ ( n ! ) ⌉ {\displaystyle \left\lceil \log _{2}(n!)\right\rceil } comparisons. This lower bound is fairly good (it can be approached within a linear tolerance by a simple merge sort), but it is known to be inexact. For example, ⌈ log 2 ⁡ ( 13 ! ) ⌉ = 33 {\displaystyle \left\lceil \log _{2}(13!)\right\rceil =33} , but the minimal number of comparisons to sort 13 elements has been proved to be 34.