The "double contour" style the capitals N, Z, Q, R, and C are written in when they are meant to mean the set of natural numbers, integers, reals, rationals, and complex numbers.

The background of this unsual style is interesting. Initially, these letters were printed in bold type. However, it is difficult to illustrate bold in handwriting, so they were written "double". This convention was then exported back into printed books, and is now a nuisance for anyone who has to typeset mathematics.

Introduced by the notable (and fictional) mathematician Bourbaki, blackboard bold or "double struck"/"open face" characters are yet another subset of the oddities that make up mathematical notation, since English, Greek, a smattering of Hebrew and assorted stylised script characters clearly aren't sufficient...

Generally they are only used to describe the classes of numbers from the naturals through to the complex, since other lecturing situations that might warrant the use of bold lend themselves to decoration (such as the underlining or addition of arrows to vectors) or are simply left unadorned for students to figure out from context. jrn points out, however, that in his lectures on physics, volume 2 (page 2-2), Feynmann suggests using blackboard bold to write the names of vectors by hand.

However, whilst blackboard bold is easier for handwriting, it's clearly less than ideal in a print/web environment. Here's how your browser attempts to render the popular symbols-

In fact, Unicode offers blackboard bold versions of the full alphabet (see page 11 of this pdf), but the above are special cases from the Letterlike Symbols block due to their more common usage.

#### Browser compatability

Contributions welcome. Thanks to zerotime, 54b, C-Dawg, Brontosaurus, LeoDV, Sir Norris, jrn and in particular WaldemarExkul for their input.

• Mozilla/ Firefox- Supports all the above, although may render as outlined letters on, for instance, MacOS X.
• Safari 2.0 (412)- Supports all the above.
• Omniweb 5.0- Supports all the above.
• Sunrise- Supports all the above.
• iCab 3.0- Supports all the above; this however is in beta, the version 2.9.8 does not. They are rendered as outlined letters.
• Camino- seems to depend on the underlying OS- I've had reports that it does not display them at all, instead producing the normal glyph twice in the above example; and that (MacOS 10.3.9) it produces outlined rather than proper blackboard bold letters, presumably in the same way iCab does.
• Lynx unsurprisingly cannot render these, but degrades to the code.
• Internet Explorer (and, by extension it seems, the E2 Offline Scratchpad)- Supports none of the above by default (may be possible to add suitable character support?), you get a blank box instead (IE6/WinXP), or a question mark (IE5/OSX).
• Slimbrowser- produces the usual blank box, followed by (UNKNOWN CHARACTER).
• Konqueror (3.3.2), despite klingon support, is reportedly stumped by these characters.

All of which suggests that for now, you'd be best sticking to a regular bold markup (probably with a short explanation on first usage) rather than using the unicode in writeups.

If you're armed with LaTeX, then adding the following to the preamble (that is, before the \begin{document}) will enable you to easily use the most common blackboard bold symbols:

\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
\DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E}
\DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A}
\DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52}
\DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51}
\DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49}
\DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43}

Then $\R$ gives you the symbol for the reals, for instance.

Alternatively, add the amsfonts package to the preamble:

\usepackage{amsfonts}
Then you'll gain access to a \mathbb{} command, such that $\mathbb{R}$ gives the symbol for the reals; this longer form is more useful if you intend to use various less common blackboard characters, since it will apply to any letter substituted for R.