Re: Size of equivalence class of Cauchy sequences


On Jan 11, 1:29 pm, "Stephen J. Herschkorn" <sjhersc...@xxxxxxxxxxxx>
wrote:
MoeBlee wrote:

So, let me see if I understand correctly: If we use the equivalence
classes of Cauchy sequences method to define real numbers, then each
real number is itself a set with cardinality that of the set of real
numbers. (?)

Yes, I think that is correct.

I know you mentioned something toward a proof, but would spell out for
me in more detail (hopefully with mainly basic set theory and not too
much real analysis, though I know that such a limitation can't be
insisted on) that each real number (equivalence class of Cauchy
sequences of rationals) has cardinality at least as great as the
cardinality of the set of real numbers?

Thanks,

MoeBlee

.

Relevant Pages

  • Re: Size of equivalence class of Cauchy sequences
    ... classes of Cauchy sequences method to define real numbers, ... But you do not have to know anything about cardinality ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
  • Re: Size of equivalence class of Cauchy sequences
    ... classes of Cauchy sequences method to define real numbers, ... But you do not have to know anything about cardinality ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... :>:>: Cantorian cardinality falls short, and it was mine, not Allan's. ... Are all the rationals computable ... a proper superset must have more elements than its proper subset. ... definition hold for finite sets and not infinite sets? ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... :>:>: Cantorian cardinality falls short, and it was mine, not Allan's. ... Are all the rationals computable ... a proper superset must have more elements than its proper subset. ... definition hold for finite sets and not infinite sets? ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :>:>: Cantorian cardinality falls short, and it was mine, not Allan's. ... Are all the rationals computable ... a proper superset must have more elements than its proper subset. ... definition hold for finite sets and not infinite sets? ...
    (sci.physics)