# Talk:Blackboard bold

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## supe

What is all that stuff with & supe at the end of the article. It is an incomplete sentence and my browser (MSIE5) displays the & supe as empty boxes. Can I delete it? -- SGBailey 2003-09-17

They appear as letters in Mozilla, so I don't think they should be deleted. In IE6, I see squares but no supes. Angela 22:19, Sep 17, 2003 (UTC)

${\displaystyle \mathbb {R} ^{n}}$

## Set inclusions

The article used to end with:

Note that PNZQ ⊆ (AR) ⊆ RCHOS.

Ah yes, an interesting math fact. We are duly impressed. But completely off-topic!
Herbee 01:13, 2004 Feb 25 (UTC)

I disagree. It helps put the symbols into context. -- Tarquin 09:19, 25 Feb 2004 (UTC)
It fails at that. The symbols that are 'put into context' aren't even Bbb. Better a good reference (e.g., to Number) than this bad example.
Herbee 16:39, 2004 Feb 25 (UTC)
In any case, its WRONG, in the sense it doesn't have a unique meaning. As a algebraic geometry person, for instance, I read P as projective space. The fact that P should actually mean primes is only thanks to the fact that I knew the subset ordering to begin with. Since the black board P entry has several meanings, the P subset should be removed altogether or somehow clarified to mean prime numbers. --Jpawloski 21:15, 27 March 2006 (UTC)
I agree that it is off-topic and should be deleted. --Zero 09:26, 25 Feb 2004 (UTC)
It's not off-topic. It makes it clear that most of the common usages of blackboard bold are related to one another. --Zundark 10:58, 25 Feb 2004 (UTC)
Well it could at least be made clear to less intelligent people like me what exactly it means :) Ragzouken 19:00, 10 December 2005 (UTC)
For so short a note, i'll argue that it warrants the space by demonstrating how the symbols are used in mathematical notation without directing the reader to another article.—Crazilla 00:11, 26 December 2005 (UTC)

The Number article has a simplified version of the statement. Interestingly, the Number article tries to explain Blackboard bold, while the Blackboard bold article tries to explain the number system. Exchanging the two would be most appropriate, I think.
Herbee 13:45, 2004 Feb 25 (UTC)

## Category:Set theory

Wouldn't something like "Mathematical notation" be better here? I see no connection to set theory, to be honest. Prumpf 23:07, 7 Sep 2004 (UTC)

## "Missing" Letters

Anyone want to comment on why the letters I, L, M, U, V, W, X, & Y aren't listed? I realize that it's probably because they aren't used, but is there anything to add to that? Should some mention be made in the text? — Preceding unsigned comment added by 128.104.112.72 (talk) 14:16, 24 Jun 2005 (UTC)

These are added, but now Arabic symbols (U+1EEA1 through U+1EEBB) are missing. TPS (talk) 01:14, 29 June 2017 (UTC)
@DMacks: Oops, thanks. 😳 TPS (talk) 01:14, 29 June 2017 (UTC)
No worries:) DMacks (talk) 02:00, 29 June 2017 (UTC)

## Great job

This article is awesome - everything I've ever wanted to know about blackboard bold. I find the origin of Z's name most interesting. I removed references to Wikipedia, since Wikipedia's use (or lack thereof) of blackboard bold isn't particularly notable, and this also violates Wikipedia: Avoid self-reference. I also used math tags for the controversial note at the bottom, because IE (used by most of our readers) doesn't render ⊆. Good job everyone. Deco 22:13, 14 July 2005 (UTC)

## B

In a computer science course, we used B as the set of binary digits (${\displaystyle \mathbb {B} =\{0,1\}}$). Can anyone confirm this usage? -- 2005 Jul 19

Yes, it is sometimes used that way (denoting the Boolean domain), although a simple uppercase B is also common. I can't find a reference at the moment (not very easy to search for) -- 2005 Aug 13

I just edited the article to include a link to boolean domain. I can confirm this usage (I've used/seen it in scholarly/peer-reviewed articles). Mathworld confirms it too. SyntaxPC(reply|contributions) 16:40, 8 April 2006 (UTC)

## G

Is it common to use the blackboard bold G for the Gaussian integers Z[i] ? I thought I did see that usage somewhere. -- KittySaturn 11:35, September 1, 2005 (UTC)

## Vectors?

The article claimed that blackboard bold letters are commonly used for vectors in physics? Anybody disagrees with my delition of this statement? The standard is to use bold and not blackboard bold letters for vectors. Older texts use a broken font, in handwriting one underlines, and sometimes one puts an arrow on top. But I've never seen a blackboard bold vector. Simon A. 13:01, 22 September 2005 (UTC)

The Feynman Lectures on Physics (at least vol. 2) uses blackboard bold as a convention for handwriting vectors, but I haven't seen that practice in any book or context released after that, so while it's possible that it was indeed common once, I agree that the current practice is to either use bold or an arrow. 91.156.57.136 (talk) 20:25, 29 April 2013 (UTC)

## ${\displaystyle \mathbb {I} }$, ${\displaystyle \mathbb {X} }$, and 1 more

In some texts (and here, for instance at Reed-Muller code) i have seen ${\displaystyle \mathbb {I} }$ used to denote indicator( function)s. (The naive set theory page uses it to denote the imaginary numbers, but this practice seems marginal.) Particularly because the notation is used in Wikipedia

I recall a texts which used ${\displaystyle \mathbb {X} }$ for arbitrary Hilbert spaces, but this may not be widespread enough to warrant mention.

One of my algebra texts (i think Artin's Algebra, but i haven't a copy at home to verify) uses ${\displaystyle \mathbb {1} }$ (which is supposed to be a blackboard-bold 1) to denote arbitrary identity elements, particularly in linear groups.

Corroborations?—Crazilla 00:04, 26 December 2005 (UTC)

I tried to add 0 and 1 to the table (see my note below) but was surprised that they came out this way. Do you know how to fix it so that it looks more like the numeral 1?
I agree, that 1 should be added for a multiplicative identity. I've seen that notation as well. --Jpawloski 21:25, 27 March 2006 (UTC)
The command \mathbb{1} fails to display the expected output because the standard Computer Modern fonts don't have a blackboard bold font defined for that symbol. The trick is to use other fonts, like mathpazo from the PSFNSS package, which include the proper symbol. The page Choice of scalable outline fonts includes some useful information on this subject. Incidentally, the symbol is also used in Allen Hatcher's algebraic topology book to refer to the identity function of whatever space he happens to be working in. --Michael Stone 04:05, 25 April 2006 (UTC)

## 0 and 1 for additive and multiplicative identities

I occassionally see blackboard 0 and 1 for identities in additive and multiplicative notation, respectively, particularly for matrix operations. Most books probably use a boldface to denote identity, but I've seen a blackboard 1 as well. Anyway I tried adding them to the table but I had to revert my edits because I couldn't get it to work. Could someone more knowledgeable perhaps intervene and add them for me? --Jpawloski 21:24, 27 March 2006 (UTC)

## Deleted "chalk" sentence

"Writing actual bold letters using chalk is simple when you turn the chalk sideways."

This advice does not help describe the topic at hand. --Charles Gaudette 19:30, 22 August 2006 (UTC)

Should there be some discussion about how blackboard bold was written on actual blackboards? It's been a few years since I was in college (class of '78), but I recall my instructors holding two pieces of chalk so that the tips were aligned horizontally. (It's trivial to do this with a pair of pencils.) The resulting lines look very similar to the typography shown in the PNG images. If anyone else can confirm this, I'd like to see it discussed in the article. --Vrmlguy (talk) 03:51, 31 August 2008 (UTC)

## Microsoft Word

Is there a way of including Blackboard Bold in microsoft word documents? I am thinking of a font, or perhaps a more obscure workaround.--Fergie 08:56, 19 September 2006 (UTC)

Well, it wasn't as easy five and a half years ago when you left your comment, but in Microsoft Word 2007, the Equation editor has Blackboard Bold. For example, in an equation type \doubleR (and then press space) to get the real number symbol. 199.46.198.233 (talk) 21:20, 5 February 2012 (UTC)

The Blackboard bold symbol defaults as the Cambria Math font which looks awkward next to Latin Modern Math. Does anyone know of the name of the font used for mathbb in LaTeX and if this can be used in Microsoft Word? Or a modification of the Latin Modern Math font that has better looking blackboard bold characters? — Preceding unsigned comment added by 2607:F140:400:2186:253B:293B:A8A0:B1CD (talk) 20:30, 17 September 2012 (UTC)

Hi Fergie - you might like to try Euclid Math Two in MS Word :-)VapourGhost (talk) 11:04, 14 August 2014 (UTC)

## Q

I (and my professors) have always written the symbol for rationals as a normal Q with a vertical line through its left side. Is this common usage, or only common usage when written, or completely uncommon? I've never seen the Q (even on math web sites) as it is shown in the article. -- Kicking222 17:44, 4 December 2006 (UTC)

A: Yes. — Preceding unsigned comment added by 75.45.240.114 (talk) 19:55, 26 November 2011 (UTC)

## TeX section

The TeX section includes this sentence:

a blackboard bold R is written as `\mathbb{R}` in regular text and as `\mathbb{R}` in math mode.

Shouldn't it be simpler? like:

a blackboard bold R is written as `\mathbb{R}`.

--89.1.57.99 08:25, 27 January 2007 (UTC)

You're right, it does seem a little strange; trawling through the history traces it to this edit, which replaced "\Bbb{R}" with "\mathbb{R}" on the grounds that "\Bbb is obsolete in amsfonts, use \mathbb instead". I'll make the change you suggested. -- Simxp 21:01, 26 May 2007 (UTC)

Normally when attempting to type a blackboard bold "1", the command is `\mathbb{1}`, but without any additional packages, this command will not produce the desired result. It is possible to use this command after adding the package `bbold`. -- Venuur, 18:14:36 September 21, 2011 (UTC) — Preceding unsigned comment added by Venuur (talkcontribs)

Other ways to write a blackboard 1 is with the use of the dsfont or the bbm package. The bbm package is (in my opinion) the best one, as it allows one to choose from three fonts. `\mathds{1}` `\mathbbm{1}` `\mathbbmss{1}` `\mathbbmtt{1}` 77.248.195.171 (talk) 18:17, 13 February 2012 (UTC)

## ${\displaystyle \mathbb {J} }$

I thought ${\displaystyle \mathbb {J} }$ was used for integers (excluding zero). 128.250.204.118 00:53, 1 May 2007 (UTC)

I encountered ${\displaystyle \mathbb {J} }$ being used for the positive and negative whole numbers and zero while being taught elementary Algebra and Calculus by a professor of mathematics. ${\displaystyle \mathbb {R} }$ or ${\displaystyle \mathbb {Z} }$ denoting the Reals, ${\displaystyle \mathbb {N} }$ the Natural, ${\displaystyle \mathbb {I} }$ the Irrational and ${\displaystyle \mathbb {Q} }$ the Rational. 124.168.146.172 (talk) 02:36, 18 June 2010 (UTC)

## ${\displaystyle \mathbb {Z} }$

I thought ${\displaystyle \mathbb {Z} }$ was used for complex numbers. 128.250.204.118 00:53, 1 May 2007 (UTC)

A: No, ${\displaystyle \mathbb {Z} }$ is used almost exclusively to represent the integers. A normal lowercase "z" is often used for an unknown complex number.

## What about blackboard ${\displaystyle \mathbb {T} }$ to designate transcendental numbers?

So that ${\displaystyle \mathbb {C} }$ = ${\displaystyle \mathbb {A} }$ U ${\displaystyle \mathbb {T} }$.

By the way, why did't you all use cut and paste to have actual blackboard bolds in your comments above, as shown below to get blackboard ${\displaystyle \mathbb {A} }$:

<"math">\mathbb{A}</"math"> but without the quotes (quotes put to deactivate processing!)

## Is this really blackboard bold?

The characters shown in this article don't look like the blackboard bold that I know. AFAIK blackboard bold are like the characters here: http://www.w3.org/TR/MathML2/double-struck.html. Matt 01:30, 21 October 2007 (UTC).

There isn't really a fixed convention for blackboard bold glyphs. The ones on that W3C page are closer to what one might use on a blackboard, but the ones shown with PNG images in the article are common in the mathematical literature. --Zundark 07:06, 21 October 2007 (UTC)

Could we include pictures of the letters actually written this way on a blackboard or whiteboard somewhere in the article?StephenJohns00 (talk) 19:27, 12 August 2018 (UTC)

## Mathematics and physics

I replaced "mathematics and physics texts" at the beginning with "mathematical texts". Blackboard bold is used all across engineering, economics, statistics, etc -- pretty much any science that uses contemporary notation. —Preceding unsigned comment added by 200.20.164.2 (talk) 16:52, 30 November 2009 (UTC)

## why no pictures of blackboard bold on actual blackboards?

? --TiagoTiago (talk) 01:50, 25 January 2010 (UTC)

## Contradiction with Another WP Article

The article Table of mathematical symbols by introduction date mentions that Blackboard bold capital Q and Z were first used by the Bourbaki Group, but this article explicitly mentions (in the Origins section, second paragraph) that that is common misconception/error. This article provides a source for this information, but it is not entirely sufficient to justify this claim. So, I have provided some citation tags in both articles until this issue of self-inconsistency within Wikipedia is remedied. Can we resolve this problem? 128.146.32.243 (talk) 19:52, 7 November 2013 (UTC)

## Not on a typewriter?

The lead notes "Blackboard bold symbols are also referred to as double struck, although they cannot actually be produced by double striking on a typewriter." By eye, these characters appear to be essentially "normal" letter and then another copy of that letter offset horizontally by a small amount. Vertical strokes are doubled, angled strokes doubled by less and only sideways not parallel to themselves, and horizontal strokes not doubled at all. That seems like exactly what one would see if one double-struck a key with a slight carriage shift between. DMacks (talk) 06:57, 12 February 2014 (UTC)

If you look at the LaTeX vs sample Unicode font, you'll see some that look like you'd describe, some that don't. But the text I think is comparing it to a double strike on a typewriter without any carriage shift. When you do that, you just get a normal bold - same outline, more ink. I think that's what most people think of as "double struck bold" on an old mechanical typewriter. SemanticMantis (talk) 19:44, 8 June 2015 (UTC)

## Why aren't the arabic letters included?

𞺡𞺢𞺣𞺥𞺦𞺧𞺨𞺩𞺫𞺬𞺭𞺮𞺯𞺰𞺱𞺲𞺳𞺴𞺵𞺶𞺷𞺸𞺹𞺺𞺻. 1234qwer1234qwer4 (talk) 12:21, 20 April 2019 (UTC)

They indeed need to be added, but I haven't an appropriate font to see what I'm doing with them. Please feel free to add, or, when I get sufficiently setup for such, I eventually will. TSamuel (talk) 14:10, 20 April 2019 (UTC)