Re: An uncountable countable set

Mike Kelly wrote:

Han de Bruijn wrote:

Mike Kelly wrote:

Han.deBruijn@xxxxxxxxxxxxxx wrote:

Mike Kelly wrote:

Infinite natural numbers. Tish and tosh. Good luck explaining that idea
to schoolkids.

Look who is talking. Good luck explaining alpha_0 to schoolkids.

Sure, the theory of infinite cardinals is beyond (most)schoolkids. But
this is a bad analogy, because school kids don't need to know about
cardinals but they do need to know how to work with natural numbers. My
point, if you really missed it, was that Tony's ideas of "infinite
natural numbers" don't match up to our "naive" or "intuitive" idea of
what numbers should be - how we were taught to do arithmetic in school.
I for one don't understand what the hell an "infinite natural number"
is. And yet supposedly the advantage of his ideas are that they're more
intuitive than a standard formal treatment.

My point is that the pot is telling the kettle that it's black (: de pot
verwijt de ketel dat ie zwart is). Your aleph_0 is in no way better than
Tony's "infinite natural number".

Your analogy is terrible, as usual.

My point was that Tony's "infinite natural numbers" are not compliant
with everyday arithmetic. Aleph_0 is part of a formalisation that leads
to an arithmetic that works exactly as we expect it to.

"... that works exactly as we expect it to". Ha, ha. Don't be silly!

Han de Bruijn

.

Loading