Transcendentals and Encryption (was Re: Nth digit of PI)

[Harald Hanche-Olsen]

+ François Pinard <pinard at iro.umontreal.ca>:

| There is an aleph1 number of real numbers

That is a statement of the continuum hypothesis, which is known to be
independent of ZFC (the Zermelo-Fraenkel set theory including the
axiom of choice, on which we tend to imagine all of modern mathematics
is based).

| and an aleph0 number of non transcendental numbers (since we can
| enumerate all algebraic equations).  Aleph1 > aleph0, an aleph1
| number of transcendental numbers remain.  Right?

For aleph1 substitute c, and all this is true (where c is the
cardinality of the continuum: c > aleph0 as Cantor showed with his
diagonal argument).

belatedly-'cause-I've-been-vacationing-in-Arizona-ly y'rs,
-- 
* Harald Hanche-Olsen     <URL:http://www.math.ntnu.no/~hanche/>
- "There arises from a bad and unapt formation of words
   a wonderful obstruction to the mind."  - Francis Bacon