Re: how to list all of the real numbers

On Aug 4, 3:13 pm, Calvin <cri...@xxxxxxxxxxxxxx> wrote:
On Aug 4, 4:39 pm, Michael Press <rub...@xxxxxxxxxxx> wrote:

Calvin exhibits two behaviors consistent with cranks,
behaviors that distinguish cranks from contributors.

* Calvin talks at length about his ideas.
* Calvin does not seek out instances of agreement.

Calvin rates above zero on the crank scale.

Those may be bad behaviors. The first is obvious, though
the second is not so obvious. But since I can be corrected
and do accept correction often, 'crank' may not be a fair
characterization. And since you used my name four times
in five lines, you may be less than perfect yourself.

The word "crank" is thrown around often on this newsgroup,
and there is much controversy to what the word means. It is
very often used to describe someone who does not fully accept
a standard set theory, such as ZFC. Ironically, the word is
most often used to describe the notorious poster JSH, yet
although JSH has contradicted standard number theory, ring
theory, etc., I have never seen him challenge set theory.

Among the nonstandard mathematicians who do contradict
standard set theory, the most commonly challenged axiom is,
of course, the Axiom of Infinity. Although ZFC with Infinity
replaced by its negation is consistent if ZFC itself is, and
there is a branch of mathematics called "finitism," it is
the general belief of most standard mathematicians that
anyone who denies Infinity in the 21st century merits the
label "crank."

Even denying Axiom of Choice, considered controversial a few
short years ago, may possibly make the Axiom's opponent a
borderline "crank." I've seen a few threads challenging
Choice recently, and the standard mathematicians who reply
in such threads defend Choice fully.

There are only a few well-known axioms which one may safely
deny without being labeled a "crank." One such axiom is the
Continuum Hypothesis. An adherent of ZFC+CH is not a "crank,"
nor is an adherent of ZFC+not CH. Also, there are the various
large cardinal axioms, some of which are supported by
different axioms. But try denying AC, or especially Infinity,
and standard mathematicians will not hesitate to use the
"crank" label.

.

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