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I often use the pattern 'I appreciate your noticing this' but recently decided it sounds strange, and switched to 'you'. (I do this with different verbs; this is just an example.) Are they both valid?
Either one is OK. The subject of a gerund complement clause may appear either in possessive form (your, his, Mr. Smith's -- this is called a POSS_-ing_ gerund complement), or in an objective (originally accusative) form (you, him, Mr. Smith -- this is called an ACC_-ing_ gerund complement). There is no grammatical difference.
Thanks, guys, very helpful comments and now I know how to describe the general version of this. To the person that downvoted the question, without comment, 30 seconds after posting: please forgive me if my expression of gratitude is less effusive.
POSS_-ing_
gerund complement), or in an objective (originally accusative) form (you, him, Mr. Smith -- this is called anACC_-ing_
gerund complement). There is no grammatical difference.