[Vocabulary] give up the idea

[Meja]

Which expression is correct: to give up the idea (of doing sth) or to give up on the idea (of doing sth)?

 

[Matthew Wai]

http://www.oxfordlearnersdictionaries.com/definition/english/give-up?q=give+up Scroll down to 'give something↔up'.
Having read the above definition, I consider 'give up the idea' correct, but I am not a teacher.

 

[Rover_KE]

Meja, please take the trouble to write something in full.

The non-standard abbreviation sth is only acceptable as a space-saver in dictionaries.

 

[Meja]

Thanks, Matthew.
I also use the former, but I wanted to check if the latter can be acceptable as well.
I know that we can say to give up on somebody when we do not expect much from that person, but I do not know if we can say give up on something.



Rover_KE, I thought that it is a standard and common abbreviation used when writing phrases, idioms, etc.

 

[Matthew Wai]

I do not know if we can say give up on something.

I think we cannot if the following definitions are correct, but I am not a teacher.
http://www.macmillandictionary.com/dictionary/british/give-up-on

 

[Matthew Wai]

Which one should I trust, COCA or the dictionary?

 

[MikeNewYork]

"Give up on something" works for me.