Re: Rational numbers, irrational numbers: each dense in real numbers

On Oct 9, 3:11 pm, David R Tribble <da...@xxxxxxxxxxx> wrote:
lwal...@xxxxxxxxx wrote:
but since there's no simple word to describe collectively
RF, TO, WM, and the others, I use the phrase "so-called."
Yesterday, I posted for the first time in the thread of yet another
opponent of mainstream mathematics, Archimedes Plutonium, and
he was very upset at my use of the word "crank" to describe him,
even with the tag "so-called." Therefore nothing is accomplished by
repeated name-calling (both sides are guilty of this).

MoeBlee wrote:
For me, it's not a matter of name-calling. I don't begrudge anyone
eschewing, rejecting, opposing, critiquing, or criticizing any
particular mathematics, including ZFC. But if someone does that in a
crank manner, then they're being a crank.

Exactly. It's not *what* they believe, it's *how* they believe.
Or, more precisely, how they present their beliefs to the
world.

There are several tell-tale indicators of crankiness; see:
http://en.wikipedia.org/wiki/Crank_%28person%29
http://tinyurl.com/8hah7

Primary among those traits is:
The true hallmark of the crank is not so much asserting
that the Earth is flat as making this assertion in the
face of all counterarguments and contrary evidence.
Certain authors who have studied the phenomenon of
crankery agree that this is the essential defining
characteristic of a crank: No argument or evidence
can ever be sufficient to make a crank abandon his belief.

I think we can safely say that this criteria applies to
several certain well-known posters to sci.math.

See also:
http://en.wikipedia.org/wiki/Duck_test

David, to argue against (some) results of ZFC I present arguments as
to why, in my opinion, ZFC is inconsistent. To argue against
Goedelian results I present arguments as to why that there are no
strong, consistent, complete (and concrete) theories is inconsistent.
To argue against results of transfinite cardinals I present arguments
as to why they are not consistent.

So, I don't carry on in the face of obvious counterexamples and
reasonable theorems. Instead, I offer justifications as to why these
contentious issues (like there isn't a universe, true doesn't mean
provable, infinite sets lack elements and aren't infinite) may
conscientiously be nullified, because of their own inconsistencies.
_Then_ I feel comfortable in the consideration of various nonstandard
theories in mathematical foundations.

Consider the physical universe, and map mathematical objects to
physical objects. Then, (all) functions among those represent
physical objects, as do functions among those, ad infinitum. Then,
there are infinitely many objects in the universe, which
mathematically is its own powerset. Then, there is realizable
evidence ("contrary evidence") that it is reasonable to discredit the
powerset result.

I found my opinion around the use of mathematical proofs to illustrate
that what I say is so.

With regards to the duck test, proper classes are defined by their
elements, as are sets. Are not proper classes defined by their
elements, containing some specified elements, as are sets, similarly
walking, quacking, etcetera?

What's your opinion about the topic under discussion: is the
specified transfinite recursion schema not defined for ordinals up to
the cardinality of the irrationals? If it's not, the irrationals
aren't uncountable. If it is, they aren't either.

Ross

--
Finlayson Consulting

.

Relevant Pages

  • PANORAMARE
    ... part of mathematics. ... The flat earth is a good approximation in your immediate ... In reality there are no infinite sets. ... An earth-centric solar system is overly complicated, ...
    (sci.math)
  • Re: infinity
    ... > Here's a way to visualize countable ordinals that might ... The point 1 is not included unless you allow infinite n, ... > Infinite sets of naturals *don't* have a largest element. ... But that isn't mathematics. ...
    (sci.math)
  • Re: infinitely many nns = infinite nns?
    ... You have no IDEA as to basic logic for mathematics. ... of set theory, and it IS shown to contradict the axioms of set theory, ... nonstandard infinite positive integer) ... that the contradictions just listed really ...
    (sci.logic)
  • Re: Suggesting a Poll
    ... exposing the scandalous fraud that is mathematics. ... rationality which we all undoubtedly possess. ... and interpreted me as saying that I, the crank AHR, disbelieve ...
    (sci.math)
  • Re: Suggesting a Poll
    ... exposing the scandalous fraud that is mathematics. ... rationality which we all undoubtedly possess. ... and interpreted me as saying that I, the crank AHR, disbelieve ...
    (sci.math)