Re: Continuum hypothesis

herbzet <herbzet@xxxxxxxxx> writes:

What do you mean by saying this sentence (CH) is true?

CH is true just in case every set of reals is countable or of the
cardinality of the continuum.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

Relevant Pages

  • Re: Mapping ordinals to the reals
    ... rationals and uncountability of the reals. ... just countably many infinities or uncountably many ... of the collection of curves to get a larger cardinality. ... conclusion of continuum many. ...
    (sci.math)
  • Re: Mapping ordinals to the reals
    ... rationals and uncountability of the reals. ... just countably many infinities or uncountably many ... of the collection of curves to get a larger cardinality. ... conclusion of continuum many. ...
    (sci.math)
  • How many continuous functions? (History)
    ... the earliest appearances of the fact that the cardinality ... We can also conclude that the aggregate of all functions ... the totality of all integrable functions of one or several ... Cantor assumes the continuum hypothesis in some of his ...
    (sci.math)
  • Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
    ... fis the position in the old sequence from which you get the n'th ... For infinite sets of labels, ... > primarily about the cardinality of the continuum and continua, ... > cardinality, and that it could be explained that way. ...
    (sci.math)
  • Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
    ... transfinite cardinality are countability vis-a-vis the cardinality of ... That's because of issues dealing with "zero ... 1/2 as the average of 1/3 and 2/3, or an infinite number of zeros is ... primarily about the cardinality of the continuum and continua, ...
    (sci.logic)