This is permissible because there is nothing in shareeah to indicate the opposite and this is not a form of worship.
Ramadan kareem is not correct, rather it should be said ‘Ramadan Mubarak

Can Saying Ramadan Mubarak/Kareem & Eid Mubarak Be Classed As Bidah? , As They Were Not The Practice Of Prophet PBUH. If So, Is It Permissible To Say Such Greetings?

Fasting | March 30, 2014 10:33 am
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My question is what is the sunnah when you greet eid greetings to someone , what should be said and how to greet , is greeting that is hugging three times is it permissible or is it considered as biddah ?
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There is a discussion amongst us about exactly how many days are the Eids celebrated according to Islam and not culture. 1 day or 3 days or more?