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To the Greeks a god was omnipotent, omnipresent, and omniscient.  Omnipotent means all powerful, omnipresent means all present,  and omniscient means all knowing.  All these things were very godlike to the Greeks.  Gods and goddesses could not die, but demigods could.

A demigod was a half-god. Demigods were created when a mortal and a god had children. These children were demigods.  Demigods had the power of gods but lived on earth as mortals.

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The A-Z Encyclopedia of Gods and Goddesses

 
Gaia, Ouranos, and the Titans

Rhea and Cronos