ℕ ⊃ℤ ⊃ℚ ⊃ℝ ⊃ℂ are without doubt more useful and more common in double-struck styles than in Fraktur styles.
But there are cases where they will be distinctly replaced by bold letters (notably when woking with homomorphic/dual sets correlated bijectively with them but having distinct projections/coordinates in a numeral set, provided that there's a defined couple of operations for compositing these coordinates with elementary base elements in the dual/homomorphic set). As soon as you start using derived styles for such notation of duals, you'll imemdiately want to use the same styles for deriving elements (numbers) of these numeral sets, so you'll get double-struck or bold or fracktur variable names and digits (notably for zero, one and i,j,k used by some other extended sets that remove some property like commutativity or distributivity of basic operations). These styles become then equivalent in functionality as diacritics or adding a prepended operator or subscripts/superscripts denoting in which set they are projected or denoting their numeral system, except that they are represented in a compact composite which is not easily decomposable. But it is still possible: ℕ ⊃ℤ ⊃ℚ ⊃ℝ ⊃ℂ could be written as well: \SetN \in SetZ \in \SetQ \in \SetR \in \SetC (TeX is commonly used for such notation when composing documents) The notation is functionaliy equivalent but it obscures notations that are already complex, so Mathematicians are inventing various shortcuts or compact representations in their text. But you can't simply treat these notations as prefered visual style, these styles have imporant strict definitions that disambiguate the meaning. These formulas also have strict layout restrictions, mich more than usual plan-text. We are in a corner case where it is just safer to consider that maths notations are not text but are binary objects that do not weok very well with the Unicode character model, and that are also far from the weak definition of symbols. Even a basic variable name 'x' is not a letter x of the Latin script, its letter case cannot be changed, it cannot be freely transliterated, and side-by-side letters do not form "words". Their grammar is in a very specific language and is highly contextual (and frequently altered by document-specific prior definitions and conventions. No plain-text algorithm will work correctly with maths notations, notably in advanced levels (not the level taught in schools for children learning arithmetic for use in daily social life). In fact I have doubts that even Unicode should make lots of efforts trying to encode that more than as an informal collection of independant symbols living in their own world, with their own script and their own "language(s)" (and there are many languages, as many as there are authors in fact and frequently more when authors invent specific languages for specific documents). For most people in the world, they can't understand the level of abstraction meant by these notations. And it is already hard for them to accept the concept of "negative" numbers and understand that the value of almost all reals are not even representable, or what a complex number means ; even the concept of multiplication of numbers is difficult to understand unless you bind it to a 2D cartesian space, and immediately they wonder what happens in their visible 3D world; then let's not speak about zeroes, or infinites or curved spaces, or fractal dimensions, or about infinitesimal quantities that are not absolutely comparable in our commonly perceived Cartesian space on which we have a limited vision... Their vision is more pragmatic: as long as they have a solution (or a tool to compute it) and it gives satisfaction in most of the cases they can perceive in their life, they will not need to go further, their vision is bound to their "experience" (and experience is not bad in itself, it is a string base for science, propagation of knowledge and utility). Most people are not probabilists, they favor statistics for remembering their experience and guide immediately their choices of action and try to explain their intents to others. 2014-06-05 10:57 GMT+02:00 Hans Aberg <[email protected]>: > On 5 Jun 2014, at 04:50, David Starner <[email protected]> wrote: > > > On Wed, Jun 4, 2014 at 6:00 AM, Jukka K. Korpela <[email protected]> > wrote: > >> The change is logical in the sense that bold face is a > >> more original notation and double-struck letters as characters imitate > the > >> imitation of boldface letters when writing by hand (with a pen or piece > of > >> chalk). > > > > On the other hand, bold face is a minor variation on normal types. > > Double-struck letters are more clearly distinct, which is probably why > > they moved from the chalkboard to printing in the first place. I don't > > see much advantage of 𝐍𝐂𝐑𝐙𝐐 over ℕℂℝℤℚ, especially when > > confusability with NCRZQ comes into play. > > The double-struck letters are useful in math, because they free other > letter styles for other use. First, only a few were used as for natural, > rational, real and complex numbers, but became popular so that all letters, > uppercase and lowercase, are now available in Unicode. > > > > _______________________________________________ > Unicode mailing list > [email protected] > http://unicode.org/mailman/listinfo/unicode >
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