# [seqfan] Re: Mathematical symbol.

Arthur O'Dwyer arthur.j.odwyer at gmail.com
Thu Oct 19 15:33:56 CEST 2023

```On Thu, Oct 19, 2023 at 5:39 AM CLAUDE DEQUATRE via SeqFan <
seqfan at list.seqfan.eu> wrote:

>
>
>   In the Shamos's catalog of the real numbers (Ed 2011), 2nd line on the top of page 301, there is this symbol: ≺ which is unknown to me.
>
> Whereas the first and the third formulas give 1.2360679774997... the 2nd one just on the right of the symbol does not.
> What is the meaning of this symbol ?
>

My first wild guess was that it stands for "approaches from above." That
is, it would mean that the right-hand side is an infinite sum, and its
partial sums are greater than the left-hand side but get asymptotically
closer to it.  (I have not fact-checked this hypothesis. If the series
actually approaches from below, or oscillating, then this can't be it.)
However, if that were a widely used notation, I'd expect it to be mentioned
e.g. here (and it's not):
https://math.stackexchange.com/questions/795537/notation-for-limit-approaching-from-above-below

https://www.quora.com/What-does-the-math-symbol-prec-mean-as-in-1-prec-log-log-n-prec-log-n
...seems to be saying that he puts it between two *series* to say "the left
one remains less-than the right one," or for converging series "the left
one converges faster than the right one"; but unfortunately that can't be
the meaning here because the left-hand side is just a constant.

My other wild hypothesis is that this symbol (which you already know is
LaTeX "\prec") is a LaTeX-typo for some other symbol that sounds like
"\prec".
Unfortunately for that hypothesis, the first search result for that
hypothesis was an example of someone typoing "\pred" when what they meant
*was* "\prec"!
https://tex.stackexchange.com/questions/164672/is-there-any-math-symbol-predeq-in-latex-how-to-use-it

my \$.02,
Arthur
```