"in" means "not", "finity" means "finish".
So infinity means endless.
eternity (outside time) is a special case of infinity.
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Four syllables in infinity.
The word you're looking for is... infinity (to go on forever)
Apeiron
Just as you have : Infinity .
Infinity is the concept of something that never ends. Obvious examples of this can be found in mathematics. A simple one would be "Limn→0 1/n".