Your sister emails you to remind you that your mother's birthday is in 2 days, because you sometimes forget birthdays. You want her to know that you didn't forget about it this time. You write back and say:
Thanks, but I would have remembered!
"Thanks" is a friendlier way to say "Thank you". Use it with people you know pretty well, like family members, friends, and coworkers who you've spoken with in the past.
Whenever you hear "I would have ___", you can always imagine that the sentence ends with "...if ___". For the example above, the speaker is trying to say "I would have remembered even if you hadn't emailed me."
"I would have ___" is used to talk about something that didn't really happen, but you're imagining how things would be different if something different had happened in the past (like if your sister hadn't reminded you of your mom's birthday). You use "would have (done)" whether the action would have happened in the past, or in the future. In the example above, your mother's birthday hasn't come yet, so you say:
I would have remembered!
But you would also say the same thing if your sister mentions that she remind you of your father's birthday six months ago:
I would have remembered that too!
A note on pronunciation: "would have" is usually pronounced "would've". Some English speakers who don't write very well make the mistake of writing this as "would of" instead of "would have".
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