Re: Review of Mueckenheims book.

In article <1172798885.715378.89490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:

On Mar 1, 12:56 pm, mueck...@xxxxxxxxxxxxxxxxx wrote:

And this subset {0, 1, 2, ..., n-1} is called n and not
{n}.

So what?

My claim, which you disputed, is correct: The identity function on
omega is a mapping from omega into the power set of omega. And you
claimed that no natural number is a member of the power set of omega,
which is incorrect (but now you're saying "of course" to the fact that
every natural number is a member of the power set of omega).

While the mapping from omega to its power set in which each element is
mapped to itself, is an injective mapping, the term "identity" when
applied to mappings usually requires a bijection with the codomain
identical to the domain. So I am a bit puzzled by why you keep applying
"identity function" to a mapping which clearly is not of this form.

The more formal description of such a mapping is an "insertion
function", which requires f(x) = x for all x in the domain, like an
identity function, but allows the domain to be a proper subset of the
codomain.

It would facilitate conversation if you would just say that you
recognize your error, so we can move on in knowledge that at least
we're on the same page as to these simple matters.

WM would not acknowledge his errors even were he able to recognize them.
.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... omega is a mapping from omega into the power set of omega. ... While the mapping from omega to its power set in which each element is ... "identity function" to a mapping which clearly is not of this form. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... omega is a mapping from omega into the power set of omega. ... While the mapping from omega to its power set in which each element is ... The identity function on w is a bijection from w onto w, ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... omega is a mapping from omega into the power set of omega. ... While the mapping from omega to its power set in which each element is ... "identity function" to a mapping which clearly is not of this form. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... omega is a mapping from omega into the power set of omega. ... f= x for all x in its domain an identity function. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... the power set of omega) exists. ... The identity function on omega is into the power set of omega, ... each member of omega is a subset of omega. ...
    (sci.math)
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