16. $2.33 \star \star$ If a positive integer has at least two digits in its decimal representation, and each digit is smaller than the digit to its right, then it is called "ascending". How many such "ascending" positive integers are there?
Parse positive integers that meet the conditions, which can be regarded as a subset of the set $S=\{1,2,3, \cdots, 9\}$ with one or more than two elements. Conversely, each subset of $S$ with two or more elements, when its elements (digits) are arranged in ascending order, also yields a positive integer that meets the conditions. The set $S$ has a total of $2^{9}=512$ subsets, among which there are 9 subsets containing only one element, and 1 empty set. Therefore, the "ascending" positive integers total $512-10=502$.