Can there be an infinity of stars in the Universe? I have a mind puzzle.

Can there be an infinity of stars in the Universe ?

I have 2 opposed reasonings, yet I don’t find any flaw in them. Can you help me here ?

Answer A : No, the number of stars cannot be infinite.

In the whole Universe, at an instant t, there are W molecules of water. This number may be very big, but it has a definite value. The same goes for stars. Each of all the stars at the instant t has her own size, and we can give her a name. We can list all of them, and we can sort them from nearest to farthest — if we are omniscient, of course.

Answer B : Yes, the number of stars can be infinite.

Space has no finite volume. Space has no ending wall. If I advance into space, I can always go further. Wherever I go, space is by default filled with… vacuum. But it could be otherwise. [I am not sure of this point.] Space could be by default filled with… air. So there would be +∞ molecules of air in the Universe. We can apply this reasoning to stars. Let’s say there is, in average, 1 star / 1060 m3. So, in the total infinite volume of space, there would be +∞ stars. When I advance into space, I would keep meeting new stars, without end. Like in these video games in which mountains keep appearing as far as you walk.
Theoretically yes, there can be infinitely many stars. Since this space you're talking about is better described by general relativity and Einstein's field equations. One of its solutions describes the universe as being spatially infinite.