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1. I forget include you on my email / in my email

2. I forget inculde your name / you in my email

3. I forget cc you on my email / in my email
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Anonymous1. I forget include you on my email / in my email

2. I forget inculde your name / you in my email

3. I forget cc you on my email / in my email

I don't think any of these is correct. How about "I forgot to include you in my email." or "I forgot to cc you in my email.
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In my email sounds better to me. It's probably more a question of convention than of a 'rule'.

At any rate, you should say 'I forget to do something'.