Heard this on a podcast today, and googled it when I got home.
You can read through all the constitutional guff if you like, but in essence, during the time between 12:00, when Bush and Cheney stepped down, and 12:01 when Biden took his oath of office, the next person in line was the Secretary of State - Condi Rice.
The first black, female president of the US.
Sorry O, but you really are (a) number two.
This is the sort of thing that will be an after-dinner argument between constitutional geeks for at least the next century.
Oh, and Obama is the 43rd president. 43 men have been president, but one of them served two terms that were separated by someone else. Grover Cleveland had something to do with it. Beats me - I don't know my US history that well.