tl;dr
It's completely the same.
Why do those four inputs produce the same output?
In unicode-math-table.tex
we find
\UnicodeMathSymbol{"02115}{\BbbN}{\mathalpha}{/bbb n, open face n}
Every Unicode code point relevant for math has a name, so that unicode-math
can do, in this case, the equivalent of
\Umathchardef`ℕ = "7 "0 "02115
(the second number could change in case range=bb
is used to select a different font for these characters).
If you add \show\mathbb
to your sample TeX file (after \begin{document}
), you'll get
> \mathbb=\long macro:
->\symbb .
This almost answers your question. At least we know that
- typing
ℕ
or \BbbN
is the same
- typing
\mathbb{N}
or \symbb{N}
is the same
It only remains to discover what's the relationship between the two cases above. Simple: \symbb{N}
does \BbbN
. Not really by chaining N
to Bbb
, but something like that (it's more complicated because one can use range=bb
to use a different font for blackboard bold letters).
Now we know that typing
$ℕ \BbbN \mathbb{N} \symbb{N}$
is exactly the same. The alias name \mathbb
for \symbb
is for backwards compatibility with older code.
Some explanation is in order. unicode-math
used to have just \mathXX
commands. However, it was realized that distinguishing between \mathXX
and \symXX
is necessary. The first form is about words used in math, the second form for single characters (and doesn't enforce ligatures if used for more characters in a row); these forms can point to different fonts. Typically, for instance, \mathbf
will use the boldface text font, whereas \symbf{x}
will use \mbfx
, pointing to U+1D431 in the math font.
While the distinction is necessary for boldface, in the case of blackboard bold there is no usage of it as a text font, so no distinction is made between \mathbb
and \symbb
, by default. You (or a package) might redefine \mathbb
to do something else (not that I recommend it).
What's the preferred form?
I'd avoid \BbbN
and probably prefer \symbb
for newer documents, unless it's possible to directly type in ℕ
.
Best Answer
You can declare both fonts, I called them
\amsmathbb
and\mathbb
here: