Of all the different explanations and interpretations people have been giving in this thread this is the most satisfying to my mathematically illiterate brain. It’s troublesome for me to grasp how 0.999… isn’t always just a bit smaller than 1 because my brain wants to think that even an infinitely tiny difference is still a difference. But when you put it like that—there’s nowhere between the two where you can draw a line between them—it seems to click in. 0.999… hugs 1 so tight that you can’t meaningfully separate them.
Of all the different explanations and interpretations people have been giving in this thread this is the most satisfying to my mathematically illiterate brain. It’s troublesome for me to grasp how 0.999… isn’t always just a bit smaller than 1 because my brain wants to think that even an infinitely tiny difference is still a difference. But when you put it like that—there’s nowhere between the two where you can draw a line between them—it seems to click in. 0.999… hugs 1 so tight that you can’t meaningfully separate them.