20060102, 06:05  #1 
Bemusing Prompter
"Danny"
Dec 2002
California
2382_{10} 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 physicsrelated Planck units, but I'm sure there's numbers much smaller. 
20060102, 06:31  #2 
Jun 2003
1,579 Posts 
Possibly some paper involving the ABC conjecture would be the answer, in my opinion.
Citrix 
20060102, 08:55  #3  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Last fiddled with by cheesehead on 20060102 at 08:57 

20060102, 10:32  #4 
Cranksta Rap Ayatollah
Jul 2003
641 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. 
20060102, 10:56  #5 
"Nancy"
Aug 2002
Alexandria
2467_{10} 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 
20060102, 14:17  #6 
Jun 2005
Near Beetlegeuse
388_{10} 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 ThueMorse constant. So maybe there aren't that many interesting small numbers.

20060102, 15:34  #7  
Jun 2005
576_{8} Posts 
Quote:
It's an interesting question, but I'm afraid I can't offer any other small constants. Drew 

20060102, 17:40  #8  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}·2,671 Posts 
Quote:
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 

20060104, 02:33  #9 
Nov 2005
2×7×13 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? :) 
20060104, 17:18  #10 
Bronze Medalist
Jan 2004
Mumbai,India
4004_{8} Posts 
smallest number in a mathematical proof?
Would 459.67 qualify ? Mally 
20060104, 22:20  #11  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:


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