Re: Review of Mueckenheims book.

On Mar 7, 9:20 pm, Virgil <vir...@xxxxxxxxxxx> wrote:

Whether that definition, or definitions in genneral, or whatever are
more technical formality does not bear upon the fact that the standard
definition in set theory textbooks of 'is a function' is what I said
it was.

Is it so in "Naive Set Theory" by Halmos?

Halmos only gives the three-place vesion, so there is no chance even
for him to dispute that the definition I gave for a one-place version.
And, though I don't have Halmos in front of me as I type, I would bet
that in the text he does make use of the principle that a function is
a relation such that for every x in the domain there is exactlhy one y
such that <x y> is an element of the function. Halmos is no
counterexample to anything I've said.

MoeBlee

.

Relevant Pages

  • Re: Review of Mueckenheims book.
    ... The fact that Halmos does not give any "one-place" definition at all ... disputes your claim that it is the standard definition. ... And it is the standard definition of 'is a function' in set theory. ... defintion of 'codomain', a function has more than one codomain. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... The fact that Halmos does not give any "one-place" definition at all ... disputes your claim that it is the standard definition. ... And it is the standard definition of 'is a function' in set theory. ... defintion of 'codomain', a function has more than one codomain. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... is your chance just to think and see that Halmos says a "relation" NOT ... relation and he doesn't say it's a triple, so my formalization may not ... is quite in keeping with ordinary set theory, ... domain, codomain, and set of ordered pairs such that etc. ...
    (sci.math)
  • Re: Theoretical/Rigorous precalculus textbook recommendation(s)
    ... Shmuel (Seymour J.) Metz wrote: ... > Halmos, "Finite Dimensional Vector Spaces" ... > If your precalculus curriculum includes set theory, ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... Is it so in "Naive Set Theory" by Halmos? ... for him to dispute that the definition I gave for a one-place version. ... disputes your claim that it is the standard definition. ...
    (sci.math)
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