chmod command use 4 digits represented as User-Owner-Others-Others, this last one are other users not in the file's group.
Each of these can have 4 (read) 2 (write) or 1 (execute), so
chmod 0 file do nothing.
If you enter
man chmod you can see how it work with the numbers.
INFO ADDED BY @Richard Nixon-
You can't remove permissions to the ROOT but what you can do is protect a file from ROOT, thus any action on this will be in vain. How to:
sudo chattr +i file
sudo chattr -i file
If you read the
/etc/passwd file you will see that the ROOT have a UID of 0.
If a user have more UID, less permission (access to critical files, programs and more) will have. You can change the UID of a user incrementing or decreasing its permissions. So in this way you could change the permissions of another user to ROOT. How to:
/etc/passwd file with
sudo vipw -s and equalizes the user permissions with the ROOT (fist on the list).
More information about the passwd file here and for vipw command type