Stop/Give up + gerund
Incorrect : The wind stopped to blow.
Correct : The wind stopped blowing.
Incorrect : He gave up to smoke.
Correct : He gave up smoking.
Note: ‘He stopped smoking’ means that he stopped the act of smoking. But when we mean to say that he stopped doing another thing in order to smoke, it is possible to say:
He stopped to smoke.
Here the infinitive indicates a purpose. However, the verb ‘cease’ may be followed by either an infinitive or a gerund.
For example:
She ceased to play the piano.
She ceased playing the piano.