Book recommendation on Dedekind's Cuts Is there any book (except Baby Rudin) where 'Dedekind's cuts' and it's consequences are explained in detailed manner with pictures (in intuitive way)?
EDIT Seems that Fikhtengol'ts's "The Fundamental of Mathematical Analysis" (Vol-1) has a little part dedicated to the Dedekind's cuts (which is in a more brain freidnly way).
 A: I have been giving this much thought recently. I have been studying Landau's book Foundations of Analysis, which through the beginning of the chapter on cuts, has no pictures. I imagine there are no pictures in the remainder of the book, either.
So it seems that it, alone, is not the book for you. But as a loose interpretation of your request, I offer Landau's book together with the following visualization of a cut that I have used, while reading it.
We start with the (positive) integers, and get progressively fancier. My visualization lives in the first quadrant of the usual plane of coordinate geometry. The primitive integers I represent as a stack of dots growing upwards. (I use the word dot to mean a point of the integer grid within the first quadrant.) In my first picture, you find $1,2,3,4,5,6$.

Notice I have drawn a ray emanating from the origin and passing through each of the dots $2/1$ and $5/1$. This is the heart of my idea --- to draw such rays in the first quadrant.
Next we get to the (positive) rational numbers. Each has an infinite number of equivalent representations, as even non-mathematicians learn rather early.

You might get the idea. Let's cheat a bit now, and consider some real numbers, and connect reals to cuts. The way I visualize a non-rational real is as a ray from the origin that is able to travel forever without striking a dot.

Now, where is a cut? I leave it to you to figure out the cut for a rational, and show the cut for the root of 2. It is simply all rays through any dot, with squared slope less than 2. Let's just show two such rays, in black, to begin.

Finally what is (the cut corresponding to) the root of two, really? The visualization follows; it is all the black rays. I prefer this to seeing a cut "on the line", because here the equivalence classes of dots (which form the rational numbers) are not erased from the picture.

A: Essays on the Theory of Numbers, a book I used to possess, goes in depth on Dedekind cuts.
It's by Richard Dedekind himself,  is a pretty good read, and I recommend it.
