My view is that this choice is best made by the reader. Personally, I tend to prefer the physical book, although for research articles, I tend to prefer electronic. As an author, since you asked, my publication royalty situation is much better with the physical book. But please choose as you like!
Out of curiosity, do you have a systematic means of choosing colors for your figures or is it a purely aesthetic judgement. (The purple/orange palette is clearly deliberate but I’m wondering how you think about use of gradients, variations of colors, etc.)
I don't have a system, but usually try out a variety of colors for a figure until I like it. I have often thought that perhaps I should be more systematic, but instead end up with a random variety. The samples here skew toward purple, but I think this is less true in the book itself. For shading and gradients, many of my infinity figures are coded with \foreach loops, which make it easy to implement a gradual change in color over successive instances.
I notice "cofinality" isn't in the index... I'm curious if you touch on that concept. I recently learned that a monotone map from an ordinal into the natural numbers is necessarily bounded above if the ordinal has uncountable cofinality, which was kind of mind-bending at first. ("You mean the map has to stop somewhere because the domain is too *big*?")
Yes, I discuss this concept in several places--but I guess it didn't make it into the index. I discuss cofinality in connection with the observations that aleph_omega being singular, whereas omega is regular, and we discuss that beth_omega is a singular strong limit cardinal, as a way of introducing the inaccessible cardinals, which would be an uncountable regular strong limit. The concept also comes up in the discussion of the orders of infinity, pointing out that no countable sequence of functions is cofinal in the order of eventual domination. Your observation about monotone maps from the ordinals is related to a similar observation about continuous functions from the long line to the reals: they must be eventually constant! Can you see the proof?
Reminds me that I have a lot to learn!
My household is having a mild debate over physical books vs. e-books. Does it matter to you, the author, which format is purchased?
My view is that this choice is best made by the reader. Personally, I tend to prefer the physical book, although for research articles, I tend to prefer electronic. As an author, since you asked, my publication royalty situation is much better with the physical book. But please choose as you like!
Out of curiosity, do you have a systematic means of choosing colors for your figures or is it a purely aesthetic judgement. (The purple/orange palette is clearly deliberate but I’m wondering how you think about use of gradients, variations of colors, etc.)
I don't have a system, but usually try out a variety of colors for a figure until I like it. I have often thought that perhaps I should be more systematic, but instead end up with a random variety. The samples here skew toward purple, but I think this is less true in the book itself. For shading and gradients, many of my infinity figures are coded with \foreach loops, which make it easy to implement a gradual change in color over successive instances.
I notice "cofinality" isn't in the index... I'm curious if you touch on that concept. I recently learned that a monotone map from an ordinal into the natural numbers is necessarily bounded above if the ordinal has uncountable cofinality, which was kind of mind-bending at first. ("You mean the map has to stop somewhere because the domain is too *big*?")
Yes, I discuss this concept in several places--but I guess it didn't make it into the index. I discuss cofinality in connection with the observations that aleph_omega being singular, whereas omega is regular, and we discuss that beth_omega is a singular strong limit cardinal, as a way of introducing the inaccessible cardinals, which would be an uncountable regular strong limit. The concept also comes up in the discussion of the orders of infinity, pointing out that no countable sequence of functions is cofinal in the order of eventual domination. Your observation about monotone maps from the ordinals is related to a similar observation about continuous functions from the long line to the reals: they must be eventually constant! Can you see the proof?