[ajkjk]

yes, I am describing imagining something. Imagine taking decimals and letting them go on without ending. That is conceptualizing them intuitively. It is easy.

I don't really know what you're arguing about. You are describing the sorts of things that have to be solved to construct them rigorously. But I don't know why. No one is talking about that.

[nilkn]

I was talking about that, specifically, the relative difficulty of defining reals from rationals vs complex numbers from reals. You replied to me. :)

Moreover, I disagree that you have imagined real numbers. I don’t think you’ve imagined a single real number at all in the manner you describe. Why should I believe you've even described anything that isn't rational to begin with? For instance, 0.999... is the same as 1. Why should I not think that whatever decimal expansion you're imagining is, similarly, equivalent to a rational number we already know about? Occam's razor would reasonably suggest you're just imagining different representations of objects already accounted for in the rationals. After all, an infinite amount of precision captured by an infinite nonrepreating string of digits could easily just converge back to a number we already know.

[ajkjk]

I am very confused why you are continually talking about rationals as if they are not real. every real number is also a rational number, in the usual conception of things, are they not? Perhaps you are distinguishing the two? like regarding 1.000 as an equivalence classes of cauchy sequences is not the same as 1.000 as the equivalence class of a/a?

because when I picture 1.000 I am clearly imagining a real number. Likewise if I imagine pi, as defined any way you like.