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Topic: distinguishability - in context, according to definitions
Replies: 43   Last Post: Feb 22, 2013 10:04 AM

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 Shmuel (Seymour J.) Metz Posts: 3,473 Registered: 12/4/04
Re: distinguishability - in context, according to definitions
Posted: Feb 19, 2013 7:50 AM

In <soOdnWuz7siUXbzMnZ2dnUVZ_rqdnZ2d@giganews.com>, on 02/17/2013
at 11:45 PM, fom <fomJUNK@nyms.net> said:

>In that book, the reflexive axiom is implemented by simply writing
>down the identity. As an axiom of identity, it will not require
>discharge. Thus, when one wants to say,

>"Let a and b be such that not a=b."

>One has in the derivation,

>a=a
>b=b
>|-(a=b)

That's not a derivation.

>0.999...=0.999...
>1.000...=1.000...
>|1.000...=0.999...
>since the assertion is that the two
>symbols are equal.

Then that assertion has to be the first step in the derivation and you
get the trivial

1.000...=0.999...
|- 1.000...=0.999...

>If one is interested in proofs that begin with quantified
>statements and that end with quantified statements, then the
>presumption is that every constant used in the proof
>is definable relative to a description.

It is quite common for a theory to include constants. They are
different from notational conventions that one defines in terms of
other symbols; their nature is constrained only by the axioms.

>It is just that the other axioms for a set theory need
>to take the universal class into account.

There are set theories in which there is no such class.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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Date Subject Author
2/10/13 fom
2/10/13 J. Antonio Perez M.
2/10/13 fom
2/11/13 Shmuel (Seymour J.) Metz
2/11/13 fom
2/14/13 Shmuel (Seymour J.) Metz
2/14/13 fom
2/14/13 fom
2/15/13 fom
2/15/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/15/13 fom
2/14/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/17/13 Barb Knox
2/18/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/21/13 fom
2/22/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/16/13 dan.ms.chaos@gmail.com
2/16/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/17/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/18/13 Shmuel (Seymour J.) Metz
2/20/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom