Aionion does not mean without beginning or end, or any variation of it,
Aionion is the adjective form of aion, aion is an age or eon, it has a beginning and an end, aionion is a quantitative term to what it modifies.
Its like the word tall, If I say " A tall man stood in front of a tall skyscraper " tall is used to describe both the man and the skyscraper, does that make the man as tall as a skyscraper ?
In Matt 25:46 eternal life is, zoen aionion, because life never-ending only is in Jesus/God, and Jesus/God are never ending so is the life.
" eternal punishment " in the Greek is kolasin aionion, the word kolasin comes from kolasis, which is a arborist term for pruning, to bring forth fruit, it is alway used for restorative punishment no retribution. Kolasis has a duration it is not never ending.
How does sin continue forever if it has been conquered by Jesus on the cross, how does death go on forever if, 1 Cor 15:28 says that the last enemy to be conquered is death, how is it conquered if it goes on forever?