Re: Distinct linear orderings on Z

From: Albert Wagner (albertwagner_at_cox.net)
Date: 03/23/05 

Date: Wed, 23 Mar 2005 12:20:56 -0600

Daryl McCullough wrote:
> Albert Wagner says...
>
>
>>I would choose (e) admit that you don't have a well-defined
>>meaning for 'infinite'
>
>
> But that's not true. The set theoretic definition of "infinite set"
> is perfectly well-defined:
>
> A set S is said to be "infinite" if
> there exists a bijection between S and a proper subset of S.

Damn. You are all mental clones of one another: totally
illiterate in English grammar and syntax. Does the official
definition actually have 'infinite' quoted?

This is not a definition of 'infinite'. Something of what you
believe concerning 'infinite' could probably be inferred from
your belief that it is a definition. But a proper definition
would not require inference of meaning, but would explicitly
state the meaning.

Look at your 'definition' restated, but without changing the
meaning: A set S is said to be infinite if a proper subset of S
is also infinite (in which case a bijection would exist).'

Or even more clearly: If S is infinite and a proper subset of S
is infinite then a bijection exists between the two.

You have actually defined 'infinite' in terms of itself, a
recursive and therefore invalid definition. The fact that you
have used careful wording to avoid explicit mention of 'infinite'
in describing a proper subset of S, only shows how duplicitous
mathematikers are. A pickpocket that works wearing gloves is not
a thief?

> What part do you think is not well-defined? This definition
> of infinite depends on a prior understanding of "proper subset"
> and "bijection".

Even worse, it depends on a prior definition of infinite, which
you apparently don't have.

> If you know what "proper subset" means, and you
> know what "bijection" means, then this definition tells you what
> "infinite" means.

No, it doesn't.

> It is hard for me to understand what you think is not well-defined
> about it.

I realize that. It is just as hard for be to believe that you
are so unwilling to explicitly define 'infinite'. One can only
assume that you know what it will reveal about your concept of
'infinite sets'. 

-- 
"I know that most men, including those at ease with
problems of the greatest complexity, can seldom
accept even the simplest and most obvious truth
if it be such as would oblige them to admit the falsity
of conclusions which they have delighted in explaining
to colleagues, which they have proudly taught to others,
and which they have woven, thread by thread,
into the fabric of their lives." -
	-- Tolstoy

Relevant Pages

  • Re: Exact-Point paradox
    ... The phrase "be infinite" has no meaning. ... a mapping from the natural numbers into the reals which is strictly ... More commonly, we model two-dimensional geometry as ordered pairs, ...
    (sci.math)
  • Re: Distinct linear orderings on Z
    ... :> meaning: A set S is said to be infinite if a proper subset of S ... :> is also infinite (in which case a bijection would exist).' ...
    (sci.math)
  • Re: Its HOW MANY TIME again sci.matht !
    ... >> Nobody in sci.math gives a crap about ... INFINITE ANSWER, WHICH IS w, NOT oo. ... that is NOT the meaning of random. ... "sequences with blanks" because you CAN'T KNOW ...
    (sci.logic)
  • Re: Evolution of Self Awareness
    ... PaulC wrote: ... Which of the infinite regressions of the ... if there is no meaning to life of the kind ...
    (talk.origins)
  • Re: infinity
    ... >>> Such an expression is called an infinite series. ... > and that it does not have meaning. ... >> He doesn't seem to make any claim about the notation, ... It is figured differently, but it is a sum nonetheless, of an infinite number ...
    (sci.math)