That is because MySQL is not running, and you can not connect to it.
If I remember well and at this moment I don't have a computer with GNU/Linux, you have to do the following:
As root:
# cd /etc/init.d
# ls
And you will find that there is a file with the name mysqld (This is if you installed mysql-server).
# ./mysqld start
And now MySQL service is up.
You can connect by typing:
$ mysql
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