Talk:e (mathematical constant)

Ongoing dissent about mnemonic format

Since there is obviously no accepted, not even a tolerated consent on having a cheap mnemonic in the formatting of a series of decimal digits of e or not, I hope to reopen an explicit discussion on this.

I found two other discussions on mnemonics for e in the archives, but they do not refer to this simple formatting of just the first groups of 5 within a lengthy report of e's decimals. As I perceive it, a grouping of decimal digits in three is widely agreed upon standard in engineering. Even the ISO-normed prefixes adhere to this. Imho, giving more than 4 digits without any grouping is inconsiderate, if not a recklessness at all. The grouping in 5 is, of course, a viable alternative, but foregoing this strict grouping, just at the very beginning, and synchronizing with it at the third group, could, imho, be a tolerable exception, when this exception yields a mnemonic, which is only objected to by a part of the editors. Additionally, I believe that a hint to the mnemonic were necssary in case of its implementation.

I do not care very much about this, but I miss the reasons for the strong aversion to the mnemonic, considering its minimal-invasive looks. Purgy (talk) 12:04, 27 January 2018 (UTC)

Based on the discussion in the section above, in which there was only mild objection to the grouping 2.7 1828 1828 45 90 45 for the first 15 digits, I went ahead and grouped it that way, and was immediately reverted for what seemed to be a rather subjective reason that it's "difficult to read". Given that this grouping appears in textbooks, I disagree that the grouping is "difficult to read"; obviously textbook authors, publishers, and students also disagree. I am also curious about the strong aversion. I have not yet seen a logical rationale for it. ~Anachronist (talk) 20:48, 27 January 2018 (UTC)

That seems like a very idiosyncratic way of grouping digits. Do other reference works really group the digits in this way? I note that Donald Knuth's Art of computer programming includes a grouping of digits that agrees with thee one given in this article. Sławomir Biały (talk) 22:03, 27 January 2018 (UTC)

Noting an extraordinary idiosyncrasy for one side of the dispute, citing just one book using the other notation, is not very argumentative in the case of minimal layout differences. Purgy (talk) 09:26, 28 January 2018 (UTC)

The grouping of digits used in the article is also used in Abramowitz and Stegun. Currently 100% of the sources cited in this discussion use the convention currently adopted in the article, with 0% of those sources favoring the proposed change. That seems like a very strong argument against this change to me. Sławomir Biały (talk) 14:28, 28 January 2018 (UTC)

Secretary problem

S%C5%82awomir_Bia%C5%82y, the new section you've added contains a true theorem statement and is titled Secretary problem, but the theorem you've written there is not the one that actually goes by that name. They both involve the floor of n/e, so maybe they are related somehow, but certainly it is not standard to use that name for this problem. --JBL (talk) 14:20, 28 January 2018 (UTC)

The cited source mentions that it is related to the secretary problem. Sławomir Biały (talk) 14:25, 28 January 2018 (UTC)

That's fine, but it's not actually the same problem. --JBL (talk) 14:34, 28 January 2018 (UTC)

Nor do we say it is. Hopefully this is now clearer in the text. Sławomir Biały (talk) 14:42, 28 January 2018 (UTC)

Comments on 'alternative characterization 6'

- The value of the quotient $f(x)/f'(x)$  being independent of $x$ for an exponential function $f$, is mentioned in the third sentence of Exponential function.
- And the property that equal absolute increments of the abscissa correspond with equal relative increments/decrements of the ordinate, is as fundamental for exponential functions. -- Hesselp (talk) 15:27, 27 April 2018 (UTC)

At least one reference that clearly and directly supports this characterization is required. Ideally, this reference should be a secondary source, showing that the characterization you gave is one that is widely used and accepted, like the others. Sławomir Biały (talk) 16:28, 27 April 2018 (UTC)

@Sławomir Biały and Joel B. Lewis ('uncited').   About references and sources:
Secondary sources of the 'alternative-6' can be found in descriptions of exponential processes (e.g. radioactive decay). As in WP:Exponential decay sentence 5-6: "The exponential time constant (or mean life time or life time, in other contexts decay time or in geometry subtangent) [...] τ is the time at which the population of the assembly is reduced to 1/e times its initial value."   Putting e in front you get essentially:  "The number e shows up as constant growth/decay factor over the life time (f/f' ) of an arbitrary exponential process (f) ".

As more primary sources, focussing on the role of the number e in all exponential processes (continuous growth/decay), I mention three articles (in Dutch, in magazines on mathematics for teachers):
- Euclides (Netherlands) 1998/99, vol. 74, no 6, p.197/8
- Wiskunde & Onderwijs ('Mathematics and teaching', Belgium) 2001, vol. 27, no 106, p. 322-325
- Euclides 2012/13, vol. 88, no 3, p. 127/8 . -- Hesselp (talk) 16:08, 28 April 2018 (UTC)

@D.Lazard. Interesting to see your modification of the first alt-6-version.
Rewriting my text into your format, I get:
If $f(t)$ is any solution of the differential equation  $y'=y/s$,  then for all $t$:    $e=f(t+s)/f(t)$.
a. My choiche of t instead of x has to do with my mixed background in physics and mathematics. In my view, an exponential function is mostly a function of time, so t. But if there are better arguments for x, excellent. The same for $f(x)$ instead of the sufficient (but still not everywhere usual?) $f$.
b. Instead of 'for all t ' and 'for all s ' in my version, you have t = 0 and s = 1.   This leads to the question: is the general case more or less difficult to grasp for a reader than the special case? (And in between there are the cases with only t=0 and with only s=1 as well.).  I don't comment on this question at the moment; only this:
c. The solutions of your differential equation are of the type  a exp(x) , not a very common type of exponential function, I think. -- Hesselp (talk) 16:08, 28 April 2018 (UTC)

I'm satisfied by the discussion at Exponential decay#Mean lifetime that something like this could be included as a characterization of e. However, I would still like to see a better source (in English!). I think some effort should be made to tie it to the articles on exponential growth and decay. I would rephrase the addition along the following lines to make that relationship clearer:

If f(t) is an exponential function, then the quantity $f(t)/f'(t)$ is a constant, sometimes called the time constant (it is the reciprocal of the exponential growth constant or decay constant). The time constant is the time it takes for the exponential function to increase by a factor of e: $f(t+\tau )=ef(t)$.

Thoughts? Sławomir Biały (talk) 19:55, 28 April 2018 (UTC)

@Sławomir Biały.  Some remarks on your proposal.
i. On "..then the quantity $f(t)/f'(t)$..".  Why 'quantity'? why not 'quotient'? Even better: simply "..then $f(t)/f'(t)$.." .
ii. On  "... $f(t)/f'(t)$ is a constant, sometimes called the time constant ..." .
The real universal constant is $f(t+\tau )/f(t)$, while $f(t)/f'(t)$ depends on $f$.  So I propose:
"... $f(t)/f'(t)$ doesn't depend on $t$ (this value is sometimes called the time constant of f(t) ) . "
iii. On  "(it is the reciprocal of the exponential growth constant or decay constant)".   This interrupts the main message, maybe better in a footnote. Or leave it out, for 'the reciprocal of a time interval' I can't see as an elementary concept.
iv. I understand that I've to wait until a sufficient number of reliable explicit secondary sources are found, for (maybe) consensus on the introduction or characterization of e as (something like)  "the stretching/shrinking factor of every exponential process (function) over any period equal to its time constant" . -- Hesselp (talk) 10:13, 29 April 2018 (UTC)

I think we should wait for native speakers of English to comment on the proposal. Some things about your critique strike me as misunderstanding idioms and grammar. Sławomir Biały (talk) 12:13, 29 April 2018 (UTC)

I like Slawomir's version. Unlike Hesselp's, it is actually possible to understand, is clearly written, and avoids obscurities. Good job getting something usable out of this. --JBL (talk) 12:58, 29 April 2018 (UTC)

Even when not a native speaker, I want to join JBL's praise of Sławomir Biały's suggestion. However, since it's about charcterizing e and not the time constant, I suggest to amend to

If f(t) is an exponential function, then $f(t)/f'(t)$ is a constant 'for all t'. quoted amendment dedicated to Hesselp 10:02, 30 April 2018 (UTC) When f describes a physical process and t is associated with time, this constant is often called the time constant $\tau$ of this process, and the reciprocal is called its exponential growth rate (>0) or decay rate (<0).

The number e is the factor by which all exponential functions change during the elapse of one time constant:

$f(t+\tau )=e\cdot f(t)$.

Honestly, I think this is mathematically obvious to a degree making additional math sources superfluous, and physics sources should abound. Purgy (talk) 15:28, 29 April 2018 (UTC)

Arguments against changing in Purgi's proposal  "...is a constant. When ... this constant is often ..."   into   "...is independent of t. When ...this value is often ..." ?   To reduce the possibility of misunderstanding.
(I know I had 'constant' as well in the first version of alternative 6.) -- Hesselp (talk) 08:36, 30 April 2018 (UTC)

Again: arguments against changing in Purgi's amended proposal:
"...is a constant 'for all t'. When ... this constant is often called the time constant $\tau$ of this process, ..."   into
"...is independent of t. When ...this value is often called time constant of the process (symbol $\tau$), ..." ?
-- Hesselp (talk) 16:05, 30 April 2018 (UTC)

I prefer Sławomir Biały's version because it does not waste time getting to the connection with e. By comparison, Purgy's version emphasizes and expands on the parts that are least closely related to the topic of this article. I suggest adding Sławomir Biały's version verbatim. --JBL (talk) 22:10, 3 May 2018 (UTC)

@JBL. Please explain what you mean with "don't randomly break equations just for kicks." (Summary 3 May 2018)
And your "More general is not better" isn't clear to me as well, for you advocate Slawomir's proposal using the most general situation. -- Hesselp (talk) 16:23, 4 May 2018 (UTC)

Seeing the bare entry now, the notable connection to time constant and decay/growth rate of exponential processes totally stripped off, I revert to D.Lazards longer standing "three"-version. Furthermore, I plead for a more explicit consensus before any other edits on this detail. Reversion already done by JBL. 06:04, 4 May 2018 (UTC) Purgy (talk) 06:00, 4 May 2018 (UTC)

Two proposals

Balancing the proposals, arguments and opinions shown on this talk page until now, could there be consensus on the following 'version 6a' ?  Arguments?  Ideas for improvement?

6a.  If f(t) is an exponential function, then $f(t)/f'(t)$ is independent of t; sometimes this value is called time constant of f(t), symbol $\tau$.  (It is the reciprocal of the exponential growth constant or decay constant.)  The time constant is the time it takes for the exponential function to increase by a factor of e. So for all t:

$e=f(t+\tau )/f(t).$

Or could there be consensus on the much shorter 'version 6b' ?  A compromise of "this only uses the concept of derivative as prerequisites", "properties of exponential functions and terminology that is unrelated with the definition of e",  "emphasizes and expands on the parts that are least closely related to the topic of this article" and "the notable connection to time constant and decay/growth rate of exponential processes totally stripped off".
Or the remark in parentheses better in a footnote? then also naming 'exponential growth constant/rate and exponential decay constant/rate?  Arguments?  Ideas for improvement?

6b.  If $f(t)$ is any solution of the differential equation $y'=y/\tau$,  (an exponential function with time constant or e-folding $\tau$), then for all $t$:

$e={\frac {f(t+\tau )}{f(t)}}.$

-- Hesselp (talk) 16:23, 4 May 2018 (UTC)

Opinion: Positive consensus is required. I will not be commenting on these specific proposals. Proposals which already seem already to have positive consensus are in the previous section, and do not require Hesselp's "improvements". Sławomir Biały (talk) 11:02, 27 May 2018 (UTC)

Known digits edit -- first million digits of E

I edited the table "Number of known decimal digits of e" to add the calculation for the first million digits of e; this information had been on this page some time ago (not added by me, BTW), and I noticed today it was gone so added it back.

This was undone with the reason "entries more recent than 1978" are "rather ridiculous." (Why are they "rather ridiculous"?) I added the information again, and noted that "This is a significant increase over the previous calculation and 1,000,000 is a notable number."

Undone again, with the (partial) comment "Already linked in external links. Secondary source needed for mention here." The external link referred to doesn't assign credit to those who computed it nor when this was done. I added the entry back with another reference as a secondary source.

Undone again, with the comment "the added source isn't particularly reliable; it's just a listing in a table on some web page, and it disagreed about the number of digits by a factor of 10 -- also, 1 million isn't a "notable number", it's just a round number."

The added source is a website maintained by two French mathematicians.

The number one million is notable enough to have its own Wikipedia page, and the one million digits of e that were calculated were used in research. Obviously, I think this is a worthwhile entry, so I added the entry again, removing the reference to the French maths site and adding references to two research articles.

Undone again, with the comment "Nothing about this entry makes it notable given the current state of affairs. Use the talk page to make your case if you must."

The current state of affairs is not relevant -- the state of affairs in 1994 is, and the calculation of e to one million digits (by two PhD astrophysicists at NASA) at that time is indeed notable; it's a significant increase over the previous result. Further, these are results that have been used in research (more recently, however, the 2-million digits of e have been used).

I hope the most recent removal of the info I attempted to add (rather, restore) is undone; the information is useful, assigns credit, and the only thing controversial about it is that a number of editors appear to want the table to end with Wozniak. Nice to be reminded (again) of why I hate editing Wikipedia pages and do it so rarely. Ciao. Owlice1 (talk) 05:26, 5 July 2018 (UTC)

A few things. First of all, the fact there's an article for 1 million is completely irrelevant. That has no bearing whatsoever on whether or not this entry should be in the list. Also, you're neglecting to mention that this entry that you want to restore is just one of a whole mess that got removed (the list has expanded and shrunk at various points). Presumably we want to draw the line somewhere. I honestly think this wouldn't be terrible if it were added back in, but these become of increasingly less historical significance as we go on. Finally, why are you so eager to restore this entry but not any of the others? –Deacon Vorbis (carbon • videos) 14:45, 5 July 2018 (UTC)

The fact that there is an article for 1 million demonstrates the number itself is indeed notable, and I posted that in response to the complaint that the number isn't notable. (If it's not a notable number, delete the page for it.) Yes, you want to draw the line somewhere, and that somewhere is at Wozniak. That's been made very clear. Nevertheless, this one additional entry is useful for the reasons I've already mentioned: it's a significant increase over the previous result, it is a notable number, it is used in research. This result came 16 years after the previous one. Other results of two million, etc., followed closely on the heels of this one, too closely, I would say, to be noted, as with the ever increasing capability in computing power and the speed at which the increases were (and are) being made, that will then always be the case: greater numbers will always be found. I've answered every criticism of the edit. As to why I didn't try to restore any others, well, we've seen how well it worked when I tried to restore just one with so much going for it! Why on earth would I bother with any others, here or anywhere else? I'm done. Owlice1 (talk) 16:06, 5 July 2018 (UTC)

It's been asserted that the 1994 calculation is notable. Notability is established by secondary sources. If this calculation is indeed noted in reliable sources, it can be restored. Sławomir Biały (talk) 16:44, 5 July 2018 (UTC)

I provided several sources, as one can see from looking at my edits. If you find none of them reliable, then please let me know what is a reliable source, and let me know, too, if you would, why this addition needs more reliable secondary sources than others listed in the table, each of which has one source, at least one of which, which is a link to a website (deemed unacceptable for my addition), doesn't work. Thanks. Owlice1 (talk) 17:21, 5 July 2018 (UTC)

While I do not feel particularly strongly on this and I am not disagreeing with Sławomir, I do believe that Purgie is making a valid point, even if a bit too flippantly. Entries in a table like this need to be more than just notable, they need to be interesting, specifically historically interesting. The table's function is to illustrate the growth of the number of known digits. It can not be complete, nor would we want it to be. It has to stop growing at some point and I think that it should stop when the next entry is no longer interesting. For years I did a corresponding lecture on the digits of π. As each new record was set I was forced to remove some items, even though they were notable at the time I started to talk about them, since they had stopped being interesting (what I could say about them I could easily have said the same about some newer entries). At this point, with over 500 trillion (I didn't really count the zeroes in Ye's table, but the number is up there) digits known, the fleeting record of the millionth digit calculation has lost all interest, at least for me. --Bill Cherowitzo (talk) 17:32, 5 July 2018 (UTC)

Yes, it has to stop growing at some point -- I do not disagree with that. I would ask, then, that those who have undone my edit defend stopping the table at 116,000 rather than 1,000,000, a number not achieved until 16 years after Wozniak's. It was after 1 million digits was reached that new significant records (2 million, 5 million, and so on) were set only months, or maybe even weeks, apart, not years. Owlice1 (talk) 17:52, 5 July 2018 (UTC)

The latest revision, with the added sources, looks reasonable to me. I say we let the addition stand. Sławomir Biały (talk) 18:06, 5 July 2018 (UTC)

I disagree with Sławomir Biały's and Owlice1's opinion that the entry under reversion should be included in the addressed table. I try to give answers to questions raised by Owlice1 and to explicate my reasons for objecting and also for my suggestion of an expanded table.

• I admit calling new records in rote computing "rather ridiculous" is quite harsh. I can only mention the "rather" as mitigating: sorry. I do believe, however, that the achieved numbers have no profound importance.
• I do not doubt the factuality of the intended entry and it being reliably sourced, but the notability of $10^{6}$ in math topics is to me just as big as any decade, perhaps slightly bigger as a multiple of $10^{3}$, favoured in technical contexts. However, I do not see any notability wrt e itself, and not even wrt a number of digits in its representation in positional number systems. There being a WP article on the number $10^{6}$ is largely irrelevant in any other article. Therefore, there is no reason, stemming from $10^{6}$ digits themselves, to appear in the article about e.
• The v. Neumann entry is relevant for the reason I tried to give: first automatically computed value. I think, v. Neumann is irrelevant in this context, the ENIAC is the relevant information, one of the first floor-sized computers, unavailable to the public. The 1961-entry might be skipped, its importance being perhaps only the increase of available digits in orders of magnitude. The 1978-entry is not important for S. Wozniak, but for the fact that then a publicly available device empowered the almost average Joe to calculate digits of almost any desired math constant to a degree, for which I have no tolerated verbiage. "Trillions" is not to my liking, because of Moore's Law and other reasons I consider obvious to most in good faith. The number of calculated digits is limited just by boredom.
• I do not deny the existence of research values in the ongoing calculations, but their nexus to e are, at least to my knowledge, confined to the application of specific algorithms, possibly exchangeable to those for other constants, which are often considered barely as useful test samples. I conjecture that even a newly discovered quantum algorithm for calculating digits of e would not justify a new entry, but only an article in WP on its own.
• I still believe that adding to the table a reason-for-notability column, containing good reasons, enhances the article. Since I was aware that my specific knowledge and active fluency in English would not be sufficient to supply really good entries there, I just did a sketchy draft, and explicitly asked for kind improvement in the edit summary.

I did not expect the qualification "flippant" (I am fully respectful!), and other reactions I consider not de rigeur. Purgy (talk) 10:15, 6 July 2018 (UTC)

The achieved result of 1,000,000 digits of e is notable. I've already pointed out a number of reasons why. I think you do not grasp this one, however: these digits were (are) available for download; this is actually useful. (Where are the 116,000 digits of e from the previous result? Published in BYTE. How useful were they? What could anyone do with them?) Generating the million digits and then publishing the result online, where the digits can be downloaded, makes them available for research. Here are three research articles that use this particular achieved result:

Ginsburg, N. and Lesner, C. (1999) "Some Conjectures about Random Numbers"

Shimojo, M., et al (2007) “A Note on Searching Digits of Circular Ratio and Napier's Number for Numerically Expressed Information on Ruminant Agriculture"

Lai, Dejian & Danca, Marius-F. (2008) "Fractal and statistical analysis on digits of irrational numbers"

Notice the last two articles mentioned were written more than a decade after these results were made available online for others to use, indicating that particular digit-set had some endurance for research (and still may, though I haven't looked for more papers using it; I have run across other papers using even the larger sets generated by Nemiroff & Bonnell, such as 2 million and 5 million digits of e, too).

Such research might not be something you'd want to do, but others clearly do. Calculating and then making these digits available online for anyone to use had not been done before. (Editing to add: at the million digit level.) Owlice1 (talk) 11:31, 6 July 2018 (UTC)

Yes, I do not grasp how often I have to ruminate that facts, typical of any irrational number, are very well notable at appropriate places, but are not notable within an article about e, which just happens to be irrational. Purgy (talk) 07:47, 7 July 2018 (UTC)

For some reason, the following comes to mind:

Who	Where	What
Colonel Mustard	Library	Wrench

I've restored Nemiroff & Bonnell to the table, with what I hope are enough references to satisfy all. Thank you for your patience. Owlice1 (talk) 11:47, 7 July 2018 (UTC)

It’s just not an interesting or remarkable result. As by 1978 it was already possible to generate over 100,000 digits on a 8-bit CPU, someone could have generated a million digits a few years later, and probably did long before 1994. There would be many such firsts that were not published as they are simply not interesting, no-one has noticed them. It really is not that interesting now anyone can download and run a program to generate digits.--JohnBlackburne^words_deeds 12:26, 7 July 2018 (UTC)

"not reliably sourced." I provided primary and secondary sources. Which of these did you find not reliable? It is certainly not true that others did not notice these results. They were used in research, the Gutenberg project published them, and the results are even available through Amazon! (The reviews are rather amusing.) The research articles using them are not about algorithms for generating e, but about how to use the generated digits. Can they, for example, be used as a random number generator, or in cryptology? That is what some of this research is, and it's clear that others must not have wanted to generate these digits themselves, as they used (and cite) these results. Speaking of "not reliably sourced," I note this from your post: someone could have generated a million digits a few years later, and probably did long before 1994. (Emphasis mine.) That's not sourced at all. I'm restoring the entry. Owlice1 (talk) 17:32, 7 July 2018 (UTC)

The computation of one million digit has not been the object of a regularly published paper. This shows that, even at the time of this computation, this was not considered by the mathematic community as a significant result. Nevertheless, the list of these digits is useful and has been used for other research. This could be mentioned elsewhere in the article, but does not belongs to this section. This list of digits is also listed in the "See also" section, which is its natural place. I have reverted your edit for these reasons.

On the other hand, when you disagree with other editors, edit-warring is the worst way for dispute resolution, as you may be blocked for editing because of the WP:3RR rule. D.Lazard (talk) 18:01, 7 July 2018 (UTC)

I rarely edit Wikipedia pages; it wasn't until this discussion that I learned the phrase "edit-warring." I brought the discussion to the talk page when it was suggested I do so, and I've answered every criticism of the edit. There was some agreement/acquiescence that the addition could stand, which is why I put it back.

BTW, I missed the "regularly published paper" for the Wozniak result that shows it is considered significant by the maths community. Where is that, please? What I see given as a source for that is a BYTE magazine article (which I probably have in the stash of old mags in the basement; I may have to go look). At least one other entry in the table has a link to a website as the source, rather than to a journal article. I have asked before why my addition, which has multiple reliable refereed secondary sources that indicate the value of this result/addition, is unacceptable while others with only one source not as robust still stand; I never got an answer to that. The goal of some of the editors appears to be to end the table at Wozniak, no matter what. Owlice1 (talk) 18:29, 7 July 2018 (UTC)

Please, improve on the given reasons

I do not think that giving reasons why which entries are given in a table degrades a featured article; maybe reasons even help the more-digits researchers. I just concede that my reasons are a bit tongue-in-cheek. I also think that "trillions" of digits of e are inappropriate in a FA. The revert first - think later approach is often really annoying.

---

Number of known decimal digits of e

Date	Decimal digits	Computation performed by	Reason for notability
1690	1	Jacob Bernoulli	First value
1714	13	Roger Cotes	First reasonable precision
1748	23	Leonhard Euler	Euler's number crunching professionality
1853	137	William Shanks	World known number cruncher
1871	205	William Shanks	... doing it again
1884	346	J. Marcus Boorman	Last known effort by rote human calculation
1949	2,010	John von Neumann (on the ENIAC)	First computerized result getting public attention
1961	100,265	Daniel Shanks and John Wrench	Hereditary deficiencies?
1978	116,000	Steve Wozniak on the Apple II	Egalitarian approach to e —The End

Since that time, the proliferation of modern high-speed desktop computers has made it possible for all those sufficiently interested and equipped with the right hardware, to compute digits of any representation of e up to the lifetime of this hardware.

References

---

Please, feel cordially invited. Purgy (talk) 09:26, 5 July 2018 (UTC)

Welcome, and thank you for your attempt to lighten up Wikipedia. However, this is an encyclopedia and articles are intended to be serious, so please don't make joke edits. Readers looking for accurate information will not find them amusing. If you'd like to experiment with editing, please use the sandbox instead, where you are given a certain degree of freedom in what you write. Template:Z175 –Deacon Vorbis (carbon • videos) 15:20, 5 July 2018 (UTC)

As for the bit about trillions, why not? It might not be the very best choice, but your proposed change is wordy, awkward, and gives no indication about the amount of digits that is reasonably attainable. –Deacon Vorbis (carbon • videos) 15:20, 5 July 2018 (UTC)

I herewith withdraw all things cordial with respect to Deacon Vorbis. He is just entitled to spit on me his condescending qualification efforts, in the same way as any IP and even vandals are entitled to edit WP.

To all those, capable to make their good faith perceiveable, I want to reinforce my cordial invitation for improvement of the suggestions I made in absolutely positive intentions. I will try to explicate these in a reply to Owlice1 above. Purgy (talk) 07:02, 6 July 2018 (UTC)