[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):

David Joyce's answer here:
...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
Unfortunately for that hypothesis, the first search result for that
hypothesis was an example of someone typoing "\pred" when what they meant
*was* "\prec"!

my $.02,

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