Law of Truly Large Numbers 20 = 1 is undecidable

 

http://mathworld.wolfram.com/LawofTrulyLargeNumbers.html

 

http://en.wikipedia.org/wiki/Law_of_Truly_Large_Numbers

 

http://skepdic.com/lawofnumbers.html

 

The Law of Truly Large Numbers is summarized nicely in the following limerick. I am not sure whether Eddington or Pound should receive credit.

 

There once was a breathy baboon

Who always breathed down a bassoon,

For he said, "It appears

That in billions of years

I shall certainly hit on a tune."

Sir Arthur Eddington (1882 1944)

 

There once was a brainy baboon

Who always breathed down a bassoon

For he said, "It appears

That in billions of years

I shall certainly hit on a tune."

Ezra Pound (1885 1972)

 

 


That 20 = 1 is the continuum hypothesis, where 0 is aleph null and 1 is aleph one.

 

http://mathworld.wolfram.com/Aleph-0.html

 

http://mathworld.wolfram.com/Aleph-1.html

 

http://en.wikipedia.org/wiki/Continuum_hypothesis

 

http://mathworld.wolfram.com/ContinuumHypothesis.html

 

Kurt Gdel proved that assuming the continuum hypothesis true does not contradict Zermelo-Fraenkel set theory. Paul Cohen proved that assuming the continuum hypothesis false does not contradict Zermelo-Fraenkel set theory. Therefore, the validity of the continuum hypothesis is undecidable within Zermelo-Fraenkel set theory.

 

The online essay You Cant Get There From Here on infinity at Platonic Realms (another site I highly recommend) is nicely done and definitely worth a look!