How much information is there in knowing the length of someone's password? If we know the password's length, it saves us from guessing any shorter passwords. For example, for a numeric password, knowing the length is 4 saves us from having to guess [blank], 0-9, 00-99 and 000-999. This lowers the number of possibilities from 1111 to 1000. The password has 90% of it's original strength. A [0-9a-zA-Z] password retains…
For any given alphabet A, and for any positive integer n, the set of strings of length n over A is a finite set, with (number of characters in A)^n elements. The set of all strings, of any length over A, is an infinite set, because it is the union of all sets of strings of length n for each positive integer n. So if you don't know the length of the password, there are infinite possibilities. If you do know the length…
Your argument therefore doesn't apply in this context.