Re: The Dedekind Snap

On Dec 15, 1:38 pm, John Jones <jonescard...@xxxxxxx> wrote:
MoeBlee wrote:
I gave you a mathematical definition of 'permutation'; you just
ignore.

The mathematical definition might want to show different symbols, but
otherwise, there's no difference between permutations and sets. I am
surprised even that there is a strict definition of sets, mathematics
being notorious for not having one.

One can define 'set' in such theories as Z set theories and NBG class
theory.

Some sets are permutations but other sets are not permutations. I gave
you the definition of 'permutation'. You simply ignore.

I gave you a mathematical definition of 'Dedekind cut', which you
ignore; it makes no mention of "falling between positional places".

Yes it does. What else does "<-> x is a Dedekind cut" supposed to mean?

I ALREADY told you.

You mean an inaccessible least upper bound. Which stretches the meaning
of 'bound', somewhat.
Please stop saying what I mean when what you say I mean is not what I
mean. When I say 'least upper bound' then that is exactly what I mean.

I like this idea of a bound being unidentifiable. A bound object that
cannot be identified is necessarily a hidden object. But then how would
we know they are there?

You're asking me a nonsense question based on your own nonsense.

Actually, the construction of the reals by Dedekind cut is completed
about halfway through Enderton's set theory book. The Mendelson book I
mentioned fills in a few of the more laborious, but quite
straightforward, details.

Do they get down to saying what it is they are doing? oR is it simply a
case of pattern reorganization?

They give ample intuitive motivation.

MoeBlee

.

Relevant Pages

  • Re: The Dedekind Snap
    ... The mathematical definition might want to show different symbols, but otherwise, there's no difference between permutations and sets. ... A bound object that cannot be identified is necessarily a hidden object. ... about halfway through Enderton's set theory book. ...
    (sci.logic)
  • Re: The Dedekind Snap
    ... The mathematical definition might want to show different symbols, ... there's no difference between permutations and sets. ... One can define 'set' in such theories as Z set theories ... What sort of definition did you have in mind? ...
    (sci.logic)
  • Re: The Dedekind Snap
    ... MoeBlee wrote: ... The mathematical definition might want to show different symbols, ... Some sets are permutations but other sets are not permutations. ... I want the reason why a definition of a set is not the same as a permutation. ...
    (sci.logic)