Leaving your computer on all the time does not damage it.
People leave computers on all the time and they are meant to stay on as the constant shutting them off and turning them back on is actually more damaging to the computer than just leaving the computer on constantly.
It is OK to leave your computer on 24 7 or all the time.
I leave 2 of my desktop computers on all the time and never shut them off.
The only time they get shut off is if the power goes out or I need to restart them.
I've left my desktop computers on 24/7 for 6 months straight before and nothing bad has happened to them.
Computers such as desktop computers are meant to operate 24 hours per day and 7 days per week.
Actually shutting the computer off and turning it back on constantly can shorten the life of the computer.
Desktop computers are best kept on and not shut off constantly.
Web servers are an example of a type of computer that are on constantly.
Those web servers run constantly so that we can access the internet and websites such as this website on.
The web servers only get shut down when needed otherwise they are on all the time.
If it's a laptop then you may want to shut it down as they can overheat more easily but desktops are cooled more easily.