[seqfan] Re: Mathematical notation

Olivier Gerard olivier.gerard at gmail.com
Thu Sep 3 08:54:47 CEST 2009

My teachers in french "college" (this would be first part of high school
for americans, age 11-14) used the following system inspired by Bourbaki
treaty's notations, that prepared us to further studies

k any field
k^* the field minus the zero element of the additive operation
\overline k : the completed field (for instance adding infinity to
a normed field)

So Z^+, Q^*, Q^+, Q^{*+}, \overline R, and all the variants applicable to
N, C, R, D (the decimal fractions) without needing any "union"

I agree that your system is more coherent and more suggestive.

It could also be extended to include concepts needed in
semigroup theory for instance.


On Thu, Sep 3, 2009 at 02:13, <franktaw at netscape.net> wrote:

> Very interesting article.
> I have a notational convenience of my own that I much prefer to the
> standard notation.  Instead of writing, for example, Q^+ (that is, Q
> with a superscript plus sign) for the positive rationals, I prefer to
> write Q^> (Q with a superscript greater than).
> The advantage of this is that I can then write Q^>= (Q with a
> superscript greater than or equal) for the non-negative rationals; and
> this is MUCH more convenient than Q^+ U {0}.  Likewise, Q^!= (Q
> superscript not equal) is the non-zero rationals -- instead of Q - {0}
> or Q^+ U Q^-.  (Q^= for {0} doesn't seem very useful, however.)
> In the case of Z for the integers, there is the alternate notation N.
> However, there seems to be some ambiguity as to whether N is supposed
> to represent Z^> or Z^>=.
> Franklin T. Adams-Watters
> -----Original Message-----
> From: Edwin Clark <eclark at math.usf.edu>
> The discussion in the paper: "Two Notes on Notation"
> by Donald Knuth at
>    http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf
> may cast some light on this subject. Although several
> of the points made in this paper were already mentioned
> in previous discussions in this thread.
> See particularly the discussion on page 6.

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