亲测有效，解决The server quit without updating PID file和Can 't connect to local MySQL server through socket

一、登陆mysql的时候报错

$ mysql -u root -p
Enter password:
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)

出现这个错误，是因为MySQL并没有启动，为了验证这个猜测，可以打开活动监视器，搜索mysqld，是无法搜到的。因为我自己是解决了问题后截图的，所以搜索的时候，mysqld进程已经启动了。

或者输入命令查看 mysql.server status

$ mysql.server status
/usr/local/mysql/support-files/mysql.server: line 365: pidof: command not found
 ERROR! MySQL is not running

可以发现，MySQL没有运行。既然MySQL没有运行，那么我们肯定要启动MySQL。

二、MySQL启动也报错

$mysql.server start
Starting MySQL
. ERROR! The server quit without updating PID file (/usr/local/var/mysql/XXXX.local.pid).

启动报错了，会不会是权限不够？于是先更改 /usr/local/var/mysql的权限

sudo chown -R _mysql:mysql /usr/local/var/mysql

权限解决之后，于是用sudo测试一下，重新启动

三、sudo启动

$ sudo mysql.server start
Password:
Starting MySQL
.. SUCCESS! 

意外的发现，MySQL启动成功了，然后再登陆mysql

$ mysql -u root -p
Enter password: 
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 2
Server version: 5.7.21-log Homebrew

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Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

总结：Can 't connect to local MySQL server through socket这个问题是由于MySQL没有启动导致的；The server quit without updating PID file是由于权限问题，解决了权限问题，第一个问题也迎刃而解。

当然由于环境配置不一样，安装方式不一样，解决方法会有些差异，但是引起问题的原因应该是一样的。我是Mac，homebrew安装的mysql，通过此方法，成功解决了问题。

参考stackoverflow上的资料：

MySql server startup error 'The server quit without updating PID file '

For a newbie: ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock'