That is the correct spelling of inevitable (unavoidable, eventual).
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If you're referring to something that there's no avoiding, the word is "inevitable." If it's something that cannot be eaten, it's "inedible."
The opposite of inevitable can be avoidable, or escapable.
Yes. "In," meaning "not." Inevitable means not avoidable.
The noun derivatives for the adjective inevitable are inevitability and inevitableness.
This is how I see it: Inevitable = Not Avoidable now or ever. Unavoidable = Not Avoidable now, but is or was avoidable at some point. For example: The saying goes "Death and Taxes are inevitable", (but that's wrong). You are born and one day you die, death is Inevitable. You may try to avoid paying taxes, but it's incredibly difficult, therefore Taxes are Unavoidable, but not quite Inevitable.