We may still have some painting to do, but for all intensive purposes, JJ's Pizza Emporium is open for business!

intents and

In this sentence "intensive" is used incorrectly. Intensive means very concentrated or focused on a specific subject. The sentence should say "for all intents and purposes". This does repeat the idea of purposes because someone's intent is their purpose, but that is the correct phrase that is commonly used. It comes from 16th century English law and means "in every practical sense".