Is "Ever Increasing" the same as "Infinite"?

After reading a certain piece of argumentation online I am currently picking a bone with the concept of infinity.

(Hidden premise)
Ever increasing is the same as infinite.

(Argument in its essence)
Atoms make up the universe.
The universe is expanding constantly.
Therefore the universe is made of infinite atoms (and by extension is infinite).

Wouldn't this call for Zeno's paradoxes, were the hidden premise true?


If the argument instead said "there is no spot in the universe where one more atom can't fit" would the universe be necessarily infinite? (And once again call for Achilles and the Turtle?)

No, "Ever Increasing" is not the same as "Infinite". Conceptually "Ever Increasing" is a term applied to a series of finite things none of which are infinite (unless one is discussing orders of infinity which is not the case here). Also it appears that the argument is based in part on a misunderstanding of what is meant by a constantly expanding universe; as a counter-example one can imagine a constantly expanding universe containing only two atoms with a constantly increasing distance between them, and at any time neither the number of particles nor the distance between them is infinite.