Infinity is a concept which has been clarified by mathematics.
Definition 1: Two sets have the same number of elements (i.e. the same cardinality), if there is a bijective map between both sets.
As a consequence the set of all natural numbers and the set of all even natural numbers have the same cardinality: Map each natural number to its double.
Definition 2: A mapset is infinite (i.e. has an infinite cardinality), if it has a proper subset of the same cardinality.
According to this definition the set of all natural numbers is infinite: It has the proper subset of even numbers which has the same cardinality.
Developing precise concepts to deal with infinite sets is due to Georg Cantor from the 19th century. It takes some time to understand his concepts and ideas about infinite sets like cardinals and ordinals. But he was the first, and his work was groundbreaking.
Aristotle accepted infinity as the possibility to go on counting (potential infinity). But Cantor accepted also infinity as a completed cardinality (actual infinity), which Aristotle did not. For a challenging introduction see infinity
Of course “infinity” is also a word from the dictionary.