I agree with above contributors in seeing a link between infinity and zero. One thing these notions have in common is that they are both deployed as if they designate quantities just when in fact they do anything but. This isn't a problem necessarily so long as we don't allow the inevitable and indeed deliberate contradictions to vex and tease us as much as they may have done to Cantor.
No, they are no more quantities than "anonymous" is a name, "homeless" an address, "stateless" a nationality, for all that we may have occasion to put these words down on a form asking for those items of information. We are simply denying the assumptions on which the requests are based, and therefore the possibility of answering them as they stand. Similarly, answering "Nothing" to "How much do you earn?" and "Infinity" to "How long should I carry on for?" or "What's the limit?" are ways not of giving quantitative answers as expected, but of declining to do so.
Elsewhere on this website, in a discussion on the Law of Nature concept, I argue that this expression too embodies a deliberate contradiction, even a jocular oxymoron not to be taken too literally or allowed to mystify us since it means the opposite or at least non-existence of what it apparently designates - a law.
In the article, George Ellis says "If a physics argument or any other argument depends on these paradoxical arguments [such as Hilbert's Hotel] it is a false argument and should be replaced by something else". I'm suggesting how such paradoxes arise in the first place.