mersenneforum.org smallest number used in a mathematical proof?
 Register FAQ Search Today's Posts Mark Forums Read

 2006-01-02, 06:05 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 45168 Posts smallest number used in a mathematical proof? We know that the largest number used in any serious proof is Graham's number. But what about the smallest number used in a mathematical proof (excluding zero and infinitesimals)? I know that there's physics-related Planck units, but I'm sure there's numbers much smaller.
 2006-01-02, 06:31 #2 Citrix     Jun 2003 157910 Posts Possibly some paper involving the ABC conjecture would be the answer, in my opinion. Citrix
2006-01-02, 08:55   #3

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·641 Posts

Quote:
 Originally Posted by ixfd64 We know that the largest number used in any serious proof is Graham's number. But what about the smallest number used in a mathematical proof (excluding zero and infinitesimals)? I know that there's physics-related Planck units, but I'm sure there's numbers much smaller.
The reciprocal of Graham's number ought to be a good candidate for the honor.

Last fiddled with by cheesehead on 2006-01-02 at 08:57

 2006-01-02, 10:32 #4 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 28116 Posts I'm guessing that it's some nonstandard analysis proof that uses an infinitesimal "infinitesimal" isn't very easy to type after a few glasses of wine.
 2006-01-02, 10:56 #5 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts I don't think there's a good answer to this question. You can always recast equations so that constants that appear in it are smaller or larger. Besides, what exactly qualifies as a constant in this context? Are the elements of a series that tends to zero constants? Alex
 2006-01-02, 14:17 #6 Numbers     Jun 2005 Near Beetlegeuse 1100001002 Posts This GreenHodge is not authoratitive, just a bloke with a blog, but he lists some numbers he thinks are interesting. After the Planck length, 1.6160*10^{-35) the next smallest number he lists is 0.412454... which he calls the Thue-Morse constant. So maybe there aren't that many interesting small numbers.
2006-01-02, 15:34   #7
drew

Jun 2005

2·191 Posts

Quote:
 Originally Posted by Numbers This GreenHodge is not authoratitive, just a bloke with a blog, but he lists some numbers he thinks are interesting. After the Planck length, 1.6160*10^{-35) the next smallest number he lists is 0.412454... which he calls the Thue-Morse constant. So maybe there aren't that many interesting small numbers.
The Planck length has units, which makes the magnitude of the number itself somewhat arbitrary. I could decide to express it in parsecs or angstroms and get vastly different values for the exact same property. Therefore, I wouldn't consider it a true 'number' in the mathematical sense in the same way that Graham's number is a very large number.

It's an interesting question, but I'm afraid I can't offer any other small constants.

Drew

2006-01-02, 17:40   #8
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

2·3·13·137 Posts

Quote:
 Originally Posted by drew The Planck length has units, which makes the magnitude of the number itself somewhat arbitrary. I could decide to express it in parsecs or angstroms and get vastly different values for the exact same property. Therefore, I wouldn't consider it a true 'number' in the mathematical sense in the same way that Graham's number is a very large number. It's an interesting question, but I'm afraid I can't offer any other small constants. Drew
There are sundry small and dimensionless quantities in physics. A famous one is the fine structure constant, which is approximately 1/137

Another and much smaller quantity is the ratio of the strengths of the gravitational and lectromagnetic interactions.

Whether physical constants have much to do with the question as originally asked is another question entirely.

Paul

 2006-01-04, 02:33 #9 nibble4bits     Nov 2005 18210 Posts What about the difference between neutrons and protons in weight, even taking account of neutrinos and electrons. Or on a similar note, what about the anticipated atomic mass and it's actual value for specific elements/isotopes? For example, helium atoms are actually a little lighter then 3(He I) or 4(He II) times the mass of a hydrogen atom. What about the probability of a broken cup suddenly reassembling itself in a tornado? :)
 2006-01-04, 17:18 #10 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22×33×19 Posts smallest number in a mathematical proof? Would -459.67 qualify ? Mally
2006-01-04, 22:20   #11

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 Originally Posted by mfgoode Would -459.67 qualify ?
"Smallest" refers to absolute magnitude, not algebraic value, or else ixfd64's "(excluding zero and infinitesimals)" wouldn't make sense.

 Similar Threads Thread Thread Starter Forum Replies Last Post literka Factoring 5 2012-01-30 12:28 jasong Math 5 2007-05-29 13:30 thommy Prime Sierpinski Project 1 2006-05-27 06:30 Fusion_power Puzzles 8 2003-11-18 19:36 wirthi Math 10 2003-10-05 13:02

All times are UTC. The time now is 01:03.

Tue May 18 01:03:32 UTC 2021 up 39 days, 19:44, 0 users, load averages: 1.24, 1.75, 2.05