What is the difference of 'forget' in these sentences?

[Anhminh1232002]

What is the difference of 'forget' in these sentences?
I forgot to lock the door.
I forgot locking the door.
I forget to lock the door.
I forget locking the door.

Thanks.

[IELTSbuddy]

As far as I can see you can't use 2 and 3:

I forgot locking the door.
I forget locking the door.

These two are just the basic difference between present and past simple:

I forgot to lock the door. = at some point in the past.
e.g. I forgot to lock the door yesterday.

I forget to lock the door. = something you may regularly do / a habit
e.g. I forget to lock the door every time I leave the house.
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[Anhminh1232002]

Hello IELTS,
How about the example given in the website http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv204.shtml
I shall never forget sharing a bottle of iced water with you beside the Pyramids in Egypt.

Is that website reliable?
Thanks.

[Jaro7788]

In my opinion:

I forgot to lock the door.

You didn't lock the door because you were paying attention to sth else at the moment.

I forgot locking the door.

Contrary to what IELTSbuddy said, I wouldn't claim this sentence is wrong. Well, it'd be rather hard to hear in everyday conversation but I would expect it to occur in, for example, a novel whose main character is a person suffering from amnesia. They might learn that the door has been locked by them (from sb else) even though no matter how hard they are trying to think, they can't recall the event in their memory.

I forget to lock the door.

Again, rather unusual in this form, but not wrong as far as grammar is concerned. I'd expect a complementary word, such as in these examples: "I often forget to lock the door" or "I tend to forget to lock the door" or "I forget to lock the door more often these days."

I forget locking the door.

Same as above - the person with amnesia is getting frustrated by the fact they constantly forget the fact they locked the door.

[Anhminh1232002]

I can see that there are two dangling ideas. Is there anyone who can give me a trusty explaination please? Hi teacher Beessness, can you give me a hand?
Thanks.

[Luschen]