From: Ilya Zakharevich <nospam-abuse_at_ilyaz.org>

Date: Thu, 12 Sep 2013 13:44:56 -0700

Date: Thu, 12 Sep 2013 13:44:56 -0700

On Thu, Sep 12, 2013 at 09:06:54PM +0300, Jukka K. Korpela wrote:

*> >And below the university level Germans
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*> >write { }, which I like better.
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*> The notation { } is quite correct.
*

IMO, in math texts the correctness is significantly less important

than being not ambiguous. (It is practically impossible to produce a

text without misprints and/or minor problems, so the readers are quite

accustomed to making corrections — as far as the context allows

EXACTLY ONE correction.)

The situation with {} is very similar to the situation with 0̸ for

the empty set and with \ for set subtraction. The Knuth's version of TeX

was designed for typesetting his books, and he (probably) did not

encounter situations where the meaning of these symbols is ambiguous.

When AMS was designing AmSTeX, the editors had experience with more

types of text, and knew solutions for these ambiguity problems: use

visually unique symbols \varnothing and \smallsetminus. (Frankly

speaking, this is my reconstruction; the symbols may have been

introduced earlier than AmSTeX.)

So:

Is {} empty set, a Poisson bracket, or the function of taking the

fractional part?

Is 0̸ the empty set, or ϕ?

Is \ the set-difference, or left-quotient?

So as far as I understand, the mathematicians who would use 0̸ and \ for ∅ and

∖ are the same people who would use DOT DOT DOT for ellipsis and won't use

\mid in {x∈ℝ||x|<1}. (\mid would typeset it similar to

{x∈ℝ | |x|<1}

.) In short: people who should know better.

*> It just isn’t an atomic symbol
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*> for the empty set but an expression consisting of the two characters
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*> “{” and “}”, with a list (here, an empty list) of elements between
*

*> them.
*

In my book, atomicity is a secondary consideration. As far as an

OpenType font typesets⁽¹⁾ "DOT DOT DOT" the same as "…", and the line

breaking algorithm won't break inside "DOT DOT DOT", I would be happy

with the non-atomic version.

⁽¹⁾ Well, one good application of … not covered by OpenType is to

visually distinguish "… ." from ". …". (Ellipsis inside a

sentence vs ellipsis inside a paragraph.)

Hope this helps,

Ilya

Received on Thu Sep 12 2013 - 15:47:14 CDT

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