I sent someone a friend request on FACEBOOK that I shouldn't have?

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If you cancelled it very quickly, then the notification on their profile will disappear... you just have to hope that they weren't paying attention to their profile when the notification appeared for those few seconds, because they may have clicked on the notification to see who added them... but they won't be able to accept it since you cancelled it.

If you Canceled the Friend Request they wont see anything as when you Cancel it the Notification Disappears for It 

The worst that can Happen at this Point is if they have Email Notifications turned on they may get a Email about it but that would be it the Actual Request would not be there tho 

Yea they will receive it even tho you cancel the request. When they pop on the request it will take them to your profile and instead of showing friend request it will say "Request Cancelled"  im sure they will understand tho