# How to read letters such as $\mathbb A$, $\mathbb B$, etc., or $\mathfrak A$, $\mathfrak B$, etc.?

This is a soft question. We can read the letters $\bf A$, $\bf B$, etc. as bold A, bold B, etc. We can read the letters $\textit{A}$, $\textit{B}$, etc. as italic A, italic B, etc. We can read the letters $\mathcal A$, $\mathcal B$, etc. as calligraphic A, calligraphic B, etc. But how do we read letters such as $\mathbb A$, $\mathbb B$, etc., or $\mathfrak A$, $\mathfrak B$, etc.?

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I think $\mathbb{A}, \mathbb{B}$ reads 'Blackboard bold A, Blackboard bold B' and $\mathfrak{A}, \mathfrak{B}$ reads 'Fraktur A, Fraktur B'. –  tetori Jan 22 '13 at 13:23
I usually just pronounce them as $A$, $B$ etc. It's rare to ''speak matematics'' without any support of written text, either in a book or on a blackboard, so it rarely causes any misunderstandings. –  mrf Jan 22 '13 at 13:23
I would say blackboard bold A or script A, respectively. –  Clayton Jan 22 '13 at 13:24
Considering the TeX language, I usually speak bb A or cal A or frak A, since we use \mathbb, \mathcal or \mathfrak. –  Sigur Jan 22 '13 at 13:35
@Clayton (and others who suggested 'script' for Gothic): How would you read $\mathscr A$? –  Asaf Karagila Jan 22 '13 at 13:36
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$\Bbb A$ is blackboard A; $\frak A$ is Gothic A.

If there is only one $A$ being used, though, we read it as A regardless to the font.

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Thanks! Indeed, there are many A's that I have to use, on the board... –  g.m. Jan 22 '13 at 13:40
That's an A? I always thought it was a U... –  Greg L Jan 22 '13 at 18:11
@Greg: Yeah, I remember finding that out... I had the exact same reaction! –  Asaf Karagila Jan 22 '13 at 18:32

If there's a reason you choose to call them all A's, there's presumably a reason why some of them are fraktur, some of them are black board, and some of them are calligraphic.

Then don't read the font. Read the meaning. For example, when I write

$g(v_1,v_2) = \langle \mathfrak{g}_1,\mathfrak{g}_2\rangle$ where $\mathfrak{g}_1,\mathfrak{g}_2\in \mathfrak{G}$ correspond to $v_1,v_2\in T_p\mathcal{G}$

italic gee of vee one and vee two is equal to the angle bracket of frak gee one and frak gee 2 where frak gee 1 and frak gee 2 belong to frak big gee and correspond to vee 1 and vee 2 in tee-pee cal gee.

That's completely incomprehensible!

The action of the metric gee on vectors vee 1 and vee 2 is set to be equal to the Killing form acting on gee 1 and gee 2, where gee 1 and gee 2 are elements of the Lie algebra gee corresponding to the tangent vectors vee 1 and vee 2 in the tangent space at point pee of the Lie group gee.

In other words, the usual reason one uses different fonts is to help distinguish between different classes of objects (and in some case isolate special objects like $\mathbb{R}$ for the real numbers). In that case, when you are reading the text, you should speak the name of the class, not the name of the font.

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Plus 10+ for this blast of common sense! –  Peter Smith Jan 22 '13 at 14:09
I beg to disagree, you're mixing up different stuff. Of course, I second with you on the general principle. But in my situation it's easier to read $\mathbb A$ as "bb A". –  g.m. Jan 22 '13 at 14:38
I see that you have voided your bladder since the comment on my comment. The point is p now, not pee. :-) –  Asaf Karagila Jan 22 '13 at 15:55
@Asaf: thanks for the correction. –  Willie Wong Jan 22 '13 at 17:01
@Asaf: you and I both know what we prefer to drink instead of water. :-) But let's cut this out. We should set an example for new users about keeping comments on topic. –  Willie Wong Jan 24 '13 at 12:02

I think it is just acceptable to say "A" and "B"...

It is quite rare that you have to read out aloud any maths that has the same letter appearing in two different fonts like this.

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Please read out loud the following sentence: $p\in\Bbb P\subseteq\mathcal P(A)$. –  Asaf Karagila Jan 22 '13 at 13:46
"Small pee is an element of pee which is a subset of the powerset of A"? –  Willie Wong Jan 22 '13 at 13:54
If I were teaching a class, I'd read that as "let p be a subset of A chosen in the family big p" (or something similar according to context) –  Andrea Mori Jan 22 '13 at 14:35
Yes but how often does such a sentence come up in everyday maths? Also usually there is a bit of context which allows you to get round having to read it exactly as it is written...for example "our subset $p$ of $A$" –  fretty Jan 24 '13 at 9:59

I find "reading" a bit vague. Are you reading those letter while lecturing? Are you reading that to a colleague out of some text? Are you reading that over the phone to somebody who is checking a TeX source file?

Different situation require different approaches.

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This seems to be a comment rather than an answer. Giving a "reading" for each of the cases you've enumerated would make for a good answer. –  robjohn Jan 22 '13 at 22:50
It's surely a cultural thing, but I've heard $\frak{A}$ referred to as "fraktur A" more frequently, although I do hear "gothic" occasionally. On a similar note, I'm increasingly hearing people actually say the names of TeX commands, even for symbols (not just fonts).
For instance, I have a professor who says "sim-eek" every time he write $\simeq$ (LaTeX command simeq.)
Depending on context, you may choose to (1) use the font name, include the style variation when applicable: "Blackboard bold A", as in this discussion: http://tex.stackexchange.com/questions/488/blackboard-bold-characters (2) use just the style variation when the font does not need to be explicitly stated: "Bold A" (3) In mathematics specifically, certain fonts of certain letters have standard usage. cf. http://en.wikipedia.org/wiki/List_of_mathematical_symbols. In this case, it would typically be read as what they mean. eg. $\mathbb P$(X)=1 might be read as "The probability of the event X occurring is equal to 1." or x $\in\mathbb N$ as "x, a natural number".