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Could you tell me the different between forget + to and forget + Ving ?
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Anonymousforget + Ving ?
I never use this, but people who do say it's the same as not remember + Ving.

I forgot to go to the meeting. = I failed to go to the meeting (because I forgot). (I did not go.)
I forgot going to the meeting. = I don't remember going to the meeting. (Maybe I did go; maybe I didn't.)

CJ
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Complete sentences would be helpful.

Forget about me. (imperative) I command you to forget about me.

I forget my brother's phone number all the time. (declarative, simple present - habituation)

May I use simple past for the comparison you request?

I forgot to set my alarm clock.

I forgot setting my alarm clock.

There is no difference.

Many (but not all) verbs may take an infinitive phrase OR a participial phrase as direct object.

I deserve to sit in the front row. She refused / declined to sit in the front row.

I deserve sitting in the front row. She refused / declined sitting in the front row.