The 'user' part of an email address (before the @) has a maximum length of 64 characters. If n is the number of non-dot characters in the user part, then only (64 - n) dots can be added to the address for it to still be valid.
The valid email addresses for that user are a subset of all 64 character combinations possible with dots, alphanumeric chars, _, and a finite set of characters that I don't remember right now. That is a finite set, therefore the subset is also finite.