Law of Truly Large Numbers – 2^À0 = À₁ 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 2^À0 = À₁ is the continuum hypothesis, where À₀ is aleph null and À₁ 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 Gödel 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 Can’t Get There From Here” on infinity at Platonic Realms (another site I highly recommend) is nicely done and definitely worth a look!