Re: My investigations into Godels Incompleteness Theorem


Peter_Smith wrote:
John Jones wrote:
The class of natural numbers is
not countable or counted, not because it supposedly goes on and on, but
because no count is internal to it, or expressed by it. They are not
ready-counted. The class of natural numbers is a set of numerals.

More crass ignorance. A class is countable if there is a bijection
between it and the class of natural numbers. So, trivially, the class
of natural numbers is countable as the identity map is trivially a
bijection.

A class is called 'countable' by virtue of it being counted. The
members of a class are not counted, and they do not count themselves -
'they' have to BE counted.

The class of natural numbers does not count itself. It has to be
counted. IF they are counted then we have a number. IF they are not
counted then we have a class. So much confusion is wrought by being
unaware of this distinction. You read it here first.

And of course the class of natural numbers is not a set of numerals.
Because if it were, natural numbers, the only members of that class,
would have to be numerals the only members of that set, and numerals
aren't numbers.

Repeatedly asserting nonsense, as you do, doesn't make it any more
impressive.

The class of natural numbers is a class of numerals.

.

Relevant Pages

  • Re: My investigations into Godels Incompleteness Theorem
    ... John Jones wrote: ... A class is countable if there is a bijection ... And of course the class of natural numbers is not a set of numerals. ... Because if it were, natural numbers, the only members of that class, ...
    (sci.logic)
  • Re: Cantors definition of set
    ... these definitions disallow a set whose individual members are ... distinct objects" in any way precludes them from also having such ... composite ... A set may have numerals as members. ...
    (sci.logic)
  • Re: Cantors definition of set
    ... these definitions disallow a set whose individual members are ... distinct objects" in any way precludes them from also having such ... composite ... A set may have numerals as members. ...
    (sci.logic)
  • Re: infinity
    ... >> While I insist that it means: ALWAYES bijection between A and B ... >> First let's define cardinality in the same way Cantor defined it. ... >> individaul properties of its members and the order they are put into. ... >> I phrase that as L is not an ordinal property of set A. ...
    (sci.math)
  • Re: infinity
    ... >>> members, but depend in some way on the actual nature of the members ... > injection of a smaller into a larger or a bijection between two of the ... > If either the number of characters in the alphabet or the string lengh ... One single maximal binary tree for both bijections. ...
    (sci.math)
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