Re: The Dedekind Snap

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.

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?


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?

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?


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Relevant Pages

  • Re: The Dedekind Snap
    ... The mathematical definition might want to show different symbols, ... about halfway through Enderton's set theory book. ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
  • Re: The Dedekind Snap
    ... The mathematical definition might want to show different symbols, ... Some sets are permutations but other sets are not permutations. ... You're asking me a nonsense question based on your own nonsense. ... 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)