Talk:Steinhaus–Moser notation

2 in a megagon

What is a megagon?? I remember a time in Wikipedia history (in late March) when Wikipedia had an article called "megagon", saying something that is completely NONSENSE, namely "The megagon is a polygon similary to Megatron in shape". It was put on Vfd and all votes were to delete. Is there anyone who can create a MEANINGFUL article of the word "megagon"?? 66.245.19.157 17:27, 19 Sep 2004 (UTC)

How large is the number being referred to as "Mega"?? How many decimal digits does it have?? 66.32.248.67 23:37, 10 Nov 2004 (UTC)

As worked out in Steinhaus polygon notation, Mega = f(f(f(...f(256)...))) [256 functions f], where f(n)=n^n.

• 256^256>10^600
• (10^600)^(10^600)=10^(600*10^600)>10^10^600
• (10^10^600)^(10^10^600)=10^((10^600)*(10^10^600))=10^10^(600+10^600)>10^10^10^600

And f has to be applied 253 times more.

The number of decimal digits is itself an extremely large number.--Patrick 00:26, Nov 11, 2004 (UTC)

Keeping base 256:

• (256^256)^(256^256)=256^256^257
• (256^256^257)^(256^256^257)=256^(256^257*256^256^257)=256^256^(257+256^257)

Patrick 00:52, Nov 11, 2004 (UTC)

Too large to name??

Are the numbers in this article also too large to name using the numbering system being talked about at the bottom of Talk:Tetration?? Graham's number I know for sure is too large for it, but I want to know if any other numbers being talked about in Wikipedia are too large. 66.245.78.117 16:29, 24 Nov 2004 (UTC)

Yes, even the number of digits of those numbers is way more than cubic plank's lengths in universe. Numbers of digits of those numbers of digits of those numbers is still big, and so on. Even the amount of times you'd have to say "number of digits of number of digits of number of digits..." is by itself number so huge, it won't fit in the known universe... The number of times you'd have to say "number of digits of number of ..." to knock down the number of times you'd have to say "number of digits of..." is still too big, even the number of times I'd have to repeat first part of this sentence is still nowhere near the size of our universe in number of plank's lengths. I could go on, but at the pace I'm explaining this right now, we'd be here till the end of universe and we'd get nowhere near it. That's why those notations are used. Deppends how deep the rabbit hole do you want to go, but those numbers are truly big. Just for comparison: 4 ^ 4 ^ 4 = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

circle = infinity

I learned that a circle has an infinite numer of corners. therefore, using the steinhaus-moser notation and the definition for the triangle/square/pentagon symbol, i would say the "number in the circle" must be an infinte number... Am i wrong? --Abdull 23:04, 30 September 2005 (UTC)

Theoretically, you would be correct. But unfortunately, when Steinhaus defined his notation, he did not nessicessarily continue in a predictable fashion, and the circle equal Moser's pentagon. Also, it is a common misconception than numbers cannot interact with infinity without becoming infinity. For instance, $x^{x^{x^{x^{x^{...}}}}}$ continuing infinitely converges to a finite value as long as:

${\frac {1}{e^{e}}}<x<{\sqrt[{e}]{e}}$ He Who Is 00:52, 8 June 2006 (UTC)

Megist(r)on

The name I remember for 10 in a circle is "megiston", not "megistron". "Megiston" also gets many more Google hits (better than an 7-to-1 ratio on megiston "large number" vs megistron "large number", and many of the hits for the latter are reflections of either this article or (surprise, surprise) MathWorld. My guess is MathWorld has simply screwed up again. I've changed the article accordingly. --Trovatore 05:18, 11 January 2006 (UTC)

Megistron is correct. "Megiston" has an other meaning. - I don't now, what a megiston is (it isn't a english word), but it isn't a number that can be write in the Steinhaus-Moser notation (Google is the proof). Google search: Megiston --93.132.201.20 (talk) 19:58, 29 May 2009 (UTC)

I believe you are incorrect. But what we need at this point is a print reference. Something not by Weisstein, obviously, since MathWorld is possibly implicated in propagating the error. --Trovatore (talk) 22:17, 30 May 2009 (UTC)

Oh, by the way, I probably do have a print ref somewhere among my unorganized books — it would be the Guinness Book of World Records, which definitely used the megiston spelling. But I can't easily put my hands on it, and anyway I can't claim it's a terribly reliable source for this sort of thing either. --Trovatore (talk) 22:20, 30 May 2009 (UTC)

Here's a reference that should settle the issue: Steinhaus, Hugo. Mathematical Snapshots. Dover. ISBN 978-0486409146.. Available from Amazon — for a hundred bucks. I'm afraid it's not worth a C-note to me to settle this. But if someone has a copy, maybe that person would be so good as to post what it says. But |this link seems to be quoting it, and uses the no-r spelling. --Trovatore (talk) 22:31, 30 May 2009 (UTC)

Time passes…

I was going to go to the paper library to have a look, but Google Books has beaten me there: ref.—Dah31 (talk) 06:34, 20 January 2017 (UTC)

Using a special program, I found that Mega's last digits are: ...6596586425189027828673870027190816633074193637388524012354109181117468059671715057145877044749894910112922449731993539660742656 Ikosarakt (talk) 16:29, 13 February 2013 (UTC)

Historical notes

I went back and checked earlier versions of Mathematical Snapshots to see when polygon notation originated. Turns out, it was introduced in the 1950 edition (checked by searches on HathiTrust on the 1938 and 1950 editions). I don't know of anyone who's managed to track down when the Moser was invented, but the Word Ways article introducing number names by Ondrejka mentions the Moser, and that was in 1968. Arcorann (talk) 03:42, 29 April 2020 (UTC)