Enable blackboard bold TeX macros \N, \Z, \Q, \R, \C for ℕ, ℤ, ℚ, ℝ, ℂ () in MathJax configuration

Question

In math, i.e. at math.stackexchange and mathoverflow, the blackboard bold symbols for:

• ℕ — Natural Numbers
• ℤ — Integers
• ℚ — Rational Numbers
• ℝ — Real Numbers
• ℂ — Complex Numbers

are used very frequently. They can be generated by $\mathbb N$ etc. for example, but TeX macros like $\N$ for $\mathbb N$would be very convenient and obvious.

For example, Wikipedia is supporting the TeX macros above in <math>-tags.

Also used frequently are:

• ℙ — integer primes and also in the context of probabilities.
• 𝔽 — the context of Galois Fields.
• ℍ — the upper complex half plane (less common).

Providing these additional macros would only require minor changes to the MathJax configuration, not to the MathJax or Markdown implementation itself.

Note: Some posts are defining their own macros, but macros can be overridden:

$\def\N{\mathbb{N}}$
$\def\N{\mathbb{A}}$
$\newcommand{\N}{\mathbb{B}}$
$\renewcommand{\N}{\mathbb{C}}$
$\N$

emits ℂ as expected. My feature request would just supply convenient defaults for some macros.

Answer 1

One important thing to keep in mind if this change is considered is whether this changes posts which already contain the macro with this name. Especially in cases where it is defined differently.

For example, people use both $\mathbf N$ (boldface N) and $\mathbb N$ (blackboard bold ℕ) for natural numbers, similarly for integers, rationals, reals. (This is explicitly mentioned in Wikipedia articles Natural number, Integer, Rational number, Real number, Complex number. This was also pointed out in the previous discussion on Mathematics Meta: $\LaTeX$ shortcuts.) It is going to be rather rare, but some people might use the macros \N, \Q, \R, \Z, \Q in different meaning.

What happens if the definition of some of the macros is added to MathJax configuration as suggested and if a post already contains definition of some of the macros, for example, $\newcommand{\N}{\mathbf N}$ (which is different from $\mathbb N$ - the one proposed in the question)? Which definition will be used after this change? (Although \mathbb N and \Bbb N are more common, you can find posts where \N is used as \mathbf N or as \mathcal N.)

I think that when changing to MathJax (or MarkDown or anything else), one should keep in mind also whether this influences how the existing posts are rendered. When some changes are applied retroactively - without user knowing that their posts are going to be changed - it is definitely not optimal.

^{The most recent change to rendering of MathJax that I am aware of was restricting the scope of \newcommand (and other commands for defining macros such as \renewcommand, \def, \let, \DeclareMathOperator) to a single post/single comment. This was changed in January 2019 as announced on Mathematics Meta. This change is also mentioned in this list: Recent feature changes to Stack Exchange. While this makes perfect sense and prevents possible clashes of macros defined in different posts, at the same time this also broke rendering of many posts and comments - which were rendered perfectly fine at the time when they were posted. You can find examples of such posts and comments on MathOverflow, on Physics and Cross Validated, but larger number of posts and comments influenced by this can be found on Mathematics.}