Because Bourbaki and Serre said so?
Sorry guys but thats the strangest justificiation Iv ever heard.
At the first place for me is understandability, which is often coupled
with common use.
Imho the \mathbb notation is the most widespread and most recognized
variant.
Another important aspect is unambiguity.
Bold big letters are often used as a variable for a group, ring, or
field, usually R for a ring. Especially in general Algebra you use the
bold big letter notation, to distuingish the algebra from the mere set
(which is non-bold).
But \mathbb R, or \mathbb Q i have never seen in a different meaning.
And even the sage abbreviation RR and QQ hint to the use of \mathbb.

On Mar 24, 8:00 pm, William Stein <wst...@gmail.com> wrote:
> On Tue, Mar 24, 2009 at 11:22 AM, John H Palmieri
>
>
>
> <jhpalmier...@gmail.com> wrote:
>
> > On Mar 24, 10:48 am, Jason Grout <jason-s...@creativetrax.com> wrote:
> >> William Stein wrote:
> >> > On Tue, Mar 24, 2009 at 9:58 AM, John H Palmieri 
> >> > <jhpalmier...@gmail.com> wrote:
> >> >> Currently the latex methods for ZZ, RR, etc. all used mathbf -- plain
> >> >> boldface -- rather than mathbb -- 'blackboard' bold. See also the (not
> >> >> currently in use) file SAGE_ROOT/devel/sage/doc/common/macros.tex:
> >> >> lots of mathbf, no mathbb.
>
> >> >> Is this an official style choice for Sage, or did it just
> >> >> spontaneously occur?
>
> >> > I "officially" chose it for the same reason I chose mathbb in all the
> >> > books/articles I wrote, which is that numerous people in publishing
> >> > convinced me that it is a better choice.
>
> >> I'm curious what the persuasive reasoning was.  I've always liked mathbb.
>
> > My impression is that people (maybe Bourbaki?) decided that bold-face
> > should be used for Z, R, etc.  Then people giving lectures wanted a
> > way to reproduce this, so someone invented blackboard bold for use on
> > a blackboard. And then the handwritten blackboard bold began to creep
> > into printed material, and we now have mathbb.  So to me it seems sort
> > of backwards to use blackboard bold when you can use ordinary bold
> > face.
>
> > Also, Wikipedia claims that Serre disapproves of the use of blackboard
> > bold in typesetting, and Serre's opinion carries some weight...
>
> Thanks John.  That's precisely the argument that influenced me long ago...
>
> William
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