Can I block my ex on Facebook?

[Jesse]

We dated 2 years ago for 2 years. Recently he's been popping up on my news feed even though we aren't friends, or I've seen him on other friend's profile's. It's frustrating to me because I used to be in love with him and trusted him more than I should have. It took me 2 years to really admit to myself how much I put him on a pedestal when I deserved better. Even though a part of me still cares about him, when I do think about him, or see him online it makes me angry. The last time I saw him in person we got along fine. I wouldn't be rude to him in person or anything, but I don't need to be reminded of him online.

Is it ridiculous to block him after 2 years? I haven't spoken to him in a year.
I don't want him to get the idea that I'm doing something childish or trying to provoke him.. I also don't want to discourage him from talking to me if he wanted to. I just need to get him out of my head.

It's frustrating how much this is affecting me...
He's been occupying my mind. And I am reminded of all the reasons why I love/hate him. These thoughts have been getting louder.
Wow, thank you so much!!

All of these answers have been very helpful!