Re: Galileo's Paradox and the Project of the Reals

In article <45996899@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

"The reals" can mean any of those versions depending on which
information from the construction from rationals you keep and which
you discard.


Um, why do you "discard" information that is readily available? Isn't
that kind of like handing out rice to fat people with gonorrhea?

No more so than discarding the meanings of words in order to alphabetize
them.

When one starts with a "bare" set, one has no internal structure implied.
As one adds more and more internal structure, like an order relation, or
a binary operation like addition, one can say a good deal more than for
the bare set.

But for bare sets, cardinalities are the best sizings one can do.
.

Relevant Pages

  • Re: Galileos Paradox and the Project of the Reals
    ... Tony Orlow wrote: ... you discard. ... When one starts with a "bare" set, one has no internal structure implied. ... the bare set. ...
    (sci.math)
  • Re: Galileos Paradox and the Project of the Reals
    ... why do you "discard" information that is readily available? ... As one adds more and more internal structure, like an order relation, or a binary operation like addition, one can say a good deal more than for the bare set. ... In that case cardinality should be a generalization of what one can say about the sizes of sets, when no order is applicable, but only set membership. ... As a general statement, it shouldn't contradict any particular statement, or it's not general. ...
    (sci.math)
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