I think there has been some confusion here. (Which explains why I feel like I am not being understood.) 3.000....00001 is not the same as 3. I meant that 3.000...000...000...000000... is the same as 3, the integer. (no final nonzero digit, just zeros to hell and back and then some more) Just as 2.9999999... is another way to write 3.

I think the crucial thing here is the infinite digits; you simply can't allow yourself to imagine the digits having an ending. Which is super-difficult because we as humans are on the whole pretty bad at imagining infinity. I mean really, really trying to imagine infinity.

I'm not very good at imagining infinity but I can work with it fairly well. Just as, say, a doctor can't really sit down and visualize everything that happens in the human body, all at once in real-time like some kind of bizzarre movie, but they will believe in it anyway and then work with the part(s) that needs working on.