[enriquto]

Both mathbbm and mathbb are wrong for number sets. These fonts look like the blackboard hack that you use to simulate boldface using chalk. On a computer you don't have this problem and you can simply use mathbf (actual boldface).

[generationP]

It might have originated as a hack, but now it's a font in its own right. Why not use it?

It's quite common to see \mathbb{R} used for the actual set of reals, while \mathbf{R} means a totally ordered field (i.e., an abstract object behaving somewhat like \mathbb{R}). The distinction is deliberate and the notation is good.

[enriquto]

> Why not use it?

Better question: why use it, when you can use the real thing?

Mathematicians concerned by typography universally use real boldface. For example: Terrence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z, Q, T, R, C.

I've never seen a boldface R to mean a set different than the real numbers. Maybe this is some fringe custom in model theory, but in mainstream mathematics it has a clear and standard meaning. Can you point me to a paper where they use a boldface R with such a meaning (i.e., different than the reals). I'm sure that this usage would always be accompanied by a clarification to avoid any confusion.

[Skeime]

True boldface has a much darker type color than blackboard bold, thus drawing your eyes to it. But usually, the occurrences of, say, the real numbers are not the most interesting or important part on the page and they thus don’t deserve that emphasis.

(Also, admittedly, I like the look of these letters.)

[danbruc]

In his papers Terence Tao is inconsistent [1][2][3], maybe because of formatting requirements? But boy is real boldface ugly [3] and sticks out like some tomato ketchup on a white wedding dress.

[1] https://arxiv.org/pdf/1611.07441.pdf

[2] https://annals.math.princeton.edu/wp-content/uploads/annals-...

[3] https://arxiv.org/pdf/math/0512114.pdf

[generationP]

Huh, it appears a lot less frequent than I thought. I had misremembered some \mathrm{R}'s as \mathbf{R}'s.

That said, I still feel that I've seen every \mathbf letter used for something other than a standard number set somewhere. But probably not in the mainstream.

[orlp]

Who is Terrence Tao? Do you mean Terence Tao?

(if we are nitpicking about typography...)

[enriquto]

Heh.

Sorry about that. A common typo. The keys are like right next to each other.

[vouaobrasil]

That would be going against the near-universal custom of using actual mathbb. They don't look like a hack to mathematicians because they are used everywhere and most people like them. Mathbf is rare and I don't recommend it.

[layer8]

How about using the Unicode characters ℕ, ℤ, ℚ, ℝ, ℂ, etc.?

[fanpu]

Interesting explanation on how it developed historically. I've seen mathbf used in some books, but I guess old conventions are hard to change.