-It is sensible that all numbers a rational, until sqrt(2) proved not to be expressible
 as a fraction.
-A story about the pythagoreans has it that Hippasus drowned at sea after discovering
 sqrt(2) irrational.
-If a state of the universe ever returns to exactly the same as it was at a previous
 time, then time is circular because the same events will occur leading to the same 
state infinitely many times, if you believe in determinism.
-Hilbert's Hotel:
Add one person to full hotel:
People in room n to room n+1, person goes to room 1
Add a bus with infinite people:
People in room n to room 2n, person in seat i goes to room 2i
Add infinite buses of infinite people:
People in room n to room 2n, person in bus j, seat i goes to room primes[j+1]^i
-Addition,Multiplication,Exponentiation,Tetration,Pentation,...
-Ackermann Generalized Exponential G(n,k,j)
G(1,a,x)=x*a, G(2,a,x)=x^a, G(3,a,x)=j tetrated to the a
Definition: G(1,k,j)=j*k
	G(n+1,1,j)=j
	G(n+1,K+1,j)=G(n,G(n+1,k,j),j)
-Transcendental: not the root of any polynomial with rational(integer) coefficients
-Grandi Series: 1-1+1-1+1-1+...
-To prove cardinality of (0,infinite) = cardinality of (0,1), map with g(x)=1/(1+x) 
This represents dividing by aleph0 since because there is one such unit interval for 
each n in the set of natural numbers. 
-Points in plane: c*c=2^(aleph0)*2^(aleph0)=2^(aleph0+aleph0)=2^(aleph0)=c
-Aleph1/Aleph0 must equal Aleph1 and not Aleph0 otherwise Aleph1 would be Aleph0*Aleph0
 which would be obtaining Aleph1 with a finite multiplication of numbers less than itself.
-Reals have a countable number of binary digits because c=2^(Aleph0) (assuming CH)
-You can fit Aleph0 finite sized objects in a plane in our universe, and Aleph0^2 in 
a surface, and Aleph0^3 in space, and Aleph0^4 by squeezing a little more, and Aleph0^n
 for any finite n by squeezing even more, but it is impossible to fit Aleph1 finite 
sized objects in the universe.
-Generalized Continuum Hypothesis by Georg Cantor: 2^(Aleph[K])=Alpeph[K+1] there is
 no way to prove this with current set theory.
-Geometry has the potential to be a complete theory since it doesn't refer to any 
specific quantities like 0. Number theory can be complete without either + or *, but
 with both it is powerful enough to never be complete (and nothing is gained by adding
 exponentiation)