Proper use of select() parameter nfds?

Greetings,

I am going over the use of select() for a server I'm writing and I
*thought* I understood the man page's description for the use of the first
parameter, nfds.

From MAN:

The first nfds descriptors are checked in each set; i.e., the descriptors
from 0 through nfds-1 in the descriptor sets are examined.

I take this to mean that each descriptor set contains n descriptors and I
am interested in examining the first nfds descriptors referenced in my
sets. I also understood it to mean that nfds has absolutely nothing to do
with the actual *value* of a descriptor, i.e. the value returned by
fopen(), socket(), etc.. Is this correct thinking? What got me
second-guessing myself was a use of select() that seems to indicate that
you have to make sure nfds is larger than the value of the largest
descriptor you want checked. Here is the select() from the questionable
code (I can provide the whole function if necessary, it's not very big):

if (select(conn->sock + 1, &input_mask, &output_mask, &except_mask,
(struct timeval *) NULL) < 0)

Is this improper use? conn->sock is set like this:

/* Open a socket */
if ((conn->sock = socket(family, SOCK_STREAM, 0)) < 0)

Any clarification on how nfds should be set would be greatly appreciated.

Thanks,
Matthew