give up
To stop trying or to let something go willingly.
To give up means to stop trying to do something or to stop believing you can succeed at it. When you give up on a difficult math problem, you put down your pencil and walk away instead of trying different approaches. When a runner gives up during a race, they stop running even though they could keep going.
Giving up is different from making a smart decision to change course. If you're trying to break through a brick wall with your bare hands, stopping isn't giving up, it's being sensible. But if you quit practicing piano after one frustrating week because a song feels too hard, that's giving up, because you know that with more practice you could learn it.
The phrase often carries a sense of surrender or defeat. In sports, a team that's losing badly might give up and stop playing with full effort. A detective might give up on solving a cold case after running out of leads.
People also use “give up” to mean surrendering something willingly. A seat on the bus can be given up to someone who needs it more. A knight might give up his sword when defeated in battle. During Lent, some people give up chocolate or video games as a form of self-discipline.