Re: An uncountable countable set

In article <451a8f41@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <45193e6f@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Well, Han, I'm not sure I agree with the statement that reconciliation
is hopeless. Is it hopeless to reconcile the wave nature of elementary
entities with their particle nature?

It is close to hopeless to expect those who reject the law of the
excluded middle (constructionists) and those who insist on it
(formalists) to agree.


If neither can appreciate the other's point, perhaps. Some christians
get along quite well with some muslims.

Only by agreeing to disagree.

The question boils down to whether 0^0 is 1.

0^0 is, in any particular context, what it is defined to be.
There are contexts in which it is more useful to have it mean 1 and
others where it is more useful to have it mean 0.





There is confusion about my "definition" of infinitesimals, because I
can see the validity both in nilpotent infinitesimals and in those that
are further infinitely divisible.

Until TO can come up with an axiom system which simultaneously allows
his infinitesimals to be both nilpotent and not, he is in trouble.


For purposes of measure on the finite scale, infinitesimals can be
considered nilpotent. That's all. Do you disagree?

I disagree that scale changes can convert between zero and non-zero.

There are approximation methods is which products of small quantities
are regarded as negligible in comparison to the quantities themselves,
but they are always just approximations.
.

Relevant Pages

  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... Is it hopeless to reconcile the wave nature of elementary entities with their particle nature? ... Until TO can come up with an axiom system which simultaneously allows his infinitesimals to be both nilpotent and not, ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... Is it hopeless to reconcile the wave nature of elementary ... his infinitesimals to be both nilpotent and not, ... But the way you seem to evaluate a limit, the sequence of staircases ...
    (sci.math)