Infinity as a concept is supported by: no matter where you draw an end point you can always +1, in perpetuity. Thus it is non-finite. So if you are unable to define and end, it is thus infinite.
The question becomes relative to your location on that line. Does infinitely large, conversely become infinitely small? Can/does infinitely large occupy the same space as infinitely small?
In Introduction to Computing Theory (senior undergrad class — why do they always label the hardest topics “Introduction to”?), we learned that there are a “countably infinite” number of integers (or natural numbers). You can enumerate them forever, without getting to the end.
However, if you consider real numbers, you can enumerate forever and never even get from 0 to 1. Therefore, this infinite is infinitely more infinite (or something, I never really did get that).
It all depends on your point of view.
From the atom's perspective, If one were standing on a nucleus of an atom, the distance to the nearest electron might seem like infinity.
To someone on a planet around Proxima Centauri the distance between the Star we call the Sun and the Earth is infinitely small, so small as not to even be detectable.
And yet, both are in the same exact space.
Unless you run out of ink. Ink is finite.