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I often attack problems on two levels, a verbal level and a visual level. At a visual level, I try to imagine how everything is related - I arrange the ingredients of the problem into a two (or sometimes three) dimensional configuration - sometimes even a movie.

I then try to reason about the configuration verbally. Like: 'Since $A$ is a proper subset of $B$, I can find $b \in B$ such that $b \notin A$. Fix any such $b$.'

However, the verbal approach suffers from the following problem: I can't distinguish $b$ from $B$, because they both sound the same, 'bee.' So I need to actually visualize those glyphs - I need to visualize $b$ and $B$. But this visualization of glyphs then interferes with the previous visualization whereby the ingredients of the problem were organized into a spatial configuration. I can't keep both images in mind at the same time.

My general question is: What can be done about this problem?

More specifically: Has anyone bothered to come up with letter names that distinguish between lowercase and uppercase? I mean, we could say 'little bee' for $b$, but that's just too many syllables.

goblin GONE
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  • I once sat through a lecture where every variable was 'a'. Whether it be a, A, $a$, $A$, $\alpha$, $\mathbb{A}$, $\mathcal{A}$, etc. Be glad you only have to contend with 2 things. – Calvin Lin May 25 '13 at 09:31
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    What's wrong with saying "small $b$", "capital $B$", "bold $\Bbb B$", "curly/scripted $\mathscr B$", "gothic (small) $\mathfrak b$"? That's short enough for me (and probably shorter than describing what these letters stand for anyway, and you'll have to do that too). – Lord_Farin May 25 '13 at 09:32
  • @Lord_Farin, yes that's what I've been trying to do. But for example, "capital bee" is four syllables, while "bee" is just one! So I find it a bit long-winded. – goblin GONE May 25 '13 at 09:40
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    26 letters simlpy is not enough. That's why mathematicians need to know greek and fraktur alphabets (really, I got confused in a lecture where someone kept referencing $\mathfrak S$ as Gee instead of Ess). For your question: Even if it has yet more syllables, speaking of "element $b$" and "set $B$" may sometimes help. – Hagen von Eitzen May 25 '13 at 10:37
  • You can also mention the type of the object explicitly relying on the common sense now and then: consider a collection bee of subsets of integers. Take a set bee in bee. A point bee in bee is called fancy if any other set bee prime in bee containing bee contains the whole set bee. This is unambiguous because all missing types can be restored in a natural way without too heavy thinking. I find it a better practice when lecturing than "small bee", "capital bee", etc. but it is a matter of taste. – fedja May 25 '13 at 13:13

1 Answers1

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Since I was effectively answering the question in the comments, I decided to move it and expand a bit.

What's wrong with saying "small $b$", "capital $B$", "bold $\Bbb B$", "curly/scripted $\mathscr B$", "gothic (small) $\mathfrak b$"?

That's short enough for me (and probably shorter than describing what these letters stand for anyway, and you'll have to do that too).

Should this not match your preferences regarding brevity then -- since I get the impression you are only "visualizing" things for yourself by talking -- you are of course entirely free to introduce some nice abbreviations (e.g. "cap $B$" for "capital $B$"), and/or some conventions (unless I say "cap", the letter is implicitly small).

I hope this is of some help.

Lord_Farin
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