Passwords: Two 50-characters vs one 100-characters In this Information Security question, we discuss whether or not a $100$ character secret randomly-generated username is equivalent to a $50$ character secret randomly-generated username plus a $50$ character secret randomly-generated password.
This answer [now deleted] claims that there is a mathematical difference.
It claims:

If we assume that the user id can be kept private and is choosen randomly, it would allow for more combinations. If we make an example with a base of $62$ possible characters to choose from $(a..z, A..Z, 0-1)$, we get:
$62^{100} = 10^{179}$ combinations [versus] $62^{50} + 62^{50} = 80^{89}$ combinations

Is this correct?
It seems erroneous to me; requiring two $50$ character items would be the same number of combinations as requiring one $100$ character item.  If I'm mistaken, can you help me understand my error?

The answer that you are referring to is incorrect, the total number of combinations will be $62^{50}\cdot 62^{50}=62^{100}$
