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The person can’t see your posts
When you block a person on Instagram that person won’t be able to see your photos, the videos you share or any of your posts.
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The person won’t be able to view your profile
When you block a person on Instagram, he won’t be able to reach your profile. If your account is set to private, the person won’t be able to locate you in search. If your account is public, the person will locate you but won’t be able to see your posts.
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The person doesn’t get notified
When you block a person on Instagram, he doesn’t get notified but he might realize that you blocked them after noticing that he can’t reach your profile anymore.
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The person can still mention you
Even after you block a person that person can still mention you in comments. The mention however won’t show up in your activity.
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They can still see your likes and comments
The blocked person will still be able to see the likes and comments you make on the profiles that person is following or the public profiles.
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Their comments and likes won’t be deleted
When you block a person, their comments and likes will not get removed from your pictures. You can manually delete the comments if you want. (See What happens when you block someone on Facebook?)
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Your likes won’t reach them
If you mistakenly like a picture of a person you blocked, the like will shortly disappear and the person won’t know that you liked the picture.
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The person will be removed from your followers
Once you block a person, they will be removed from your followers list.
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You won’t be able to message each other
When you block someone on Instagram, both you and that person won’t be able to exchange private messages. (See What happens when you block someone on Whatsapp?)