This is mind blowing. I think that it also illustrates what we're talking about and how difficult it is to convey concepts through writing and symbols. The Hilbert's Hotel thought experiment is one way to think about the concept of infinity using mathematics and logic. It delights and surprises when we get it, but having experienced a sense of infinity in the past, I can say that both experiences differ. Now, you can take the idea of infinity and use different arrangement of symbols to convey the idea. In this case poetry:

“To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.””
― William Blake

I enjoyed this poem when I first read it, but I never "experienced it" or "grasped its meaning" until I programmed a psychedelic session with poetry and experienced a sense of infinity in this timeless moment. Only then, I felt that I truly understood that poem. And it blew my mind to the extent that I felt a ecstatic bliss when I read it again while under the influence of psychedelics. But here we have another conundrum, now I'm trying to use words to convey the meaning and experience of that internal psychological experience. Another room in Hilbert's Hotel. That is, I'm trying to use words to convey my understanding of Hilbert's Hotel by using words written centuries ago, so that I can use more words to explain an internal state to try to convey my meaning using more words. I keep moving from room to room, in a manner of speaking. It never ends and hence it's truly infinite (or fractal to use even more words and concepts) 🙃