arrivederci has 4 terms in it:
a - ri - vedere -ci
a: to (expresses a wish)
ri: again (as a prefix usually means repetition)
vedere: to see
ci: us (an an object)
Therefore it is a way of saying goodbye expressing intention to meet again, usually when the 'lei' form is used
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ciao has an interesting etimology, and is used when the 'tu' form is used, both
when meeting or going away; usually friends use 'ciao' or 'a presto' (see you soon),
but not 'arrivederci'.