## Tuesday, December 1, 2009

### Cranks and crackpots

This guy seems coherent enough at first glance: Are real numbers uncountable?

Ian said...

Mark Chu-Carroll has tackled this same nonsense, either from the same individual or an equally clueless contributor: http://scienceblogs.com/goodmath/2009/01/the_continuum_hypothesis_solve.php

Aaron said...

Can I up-vote the comment? It took me less time to undertand Mark's post than to finish _reading_ the original one.

I particularly like how he chose two number bases, showed an example of a finitely sequence named number (0.3 in base 9) can name an infinite sequence named number (0.3333.. in 10), and somehow that example is supposed to prove that you can construct any real number.

Correct me if I'm wrong, but that doesn't seem to even suggests it's possible to change between bases using this naming scheme -- base 10's tree used up all the natural numbers, leaving none for those infinite digit base 9 numbers. 0.3 base 9 is covered, but what about 0.333333.. base 9, also called 3/8ths.

ddzuk said...

@Aaron: 1/3 isn't really a problem despite the fact that his answer to it doesn't make a lot of sense. you can finitely represent a periodic decimal number by adding a symbol to the alphabet you are using, for example. The problem is with numbers that have an infinite representation *without* repeating, you can not handle those because they make the depth of that tree infinite.
he seems to have problems accepting numbers accepting those things but if that's his problem then he should be questioning the existence of things like sqrt(2) and pi...