Re: An uncountable countable set

Virgil wrote:
In article <45203919@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:



Since ordinals are, by definition, well ordered, they cannot contain any
endlessly decreasing sequences, which TO's models require.
Neither can the reals.

How about the set of negative integers? How is that not an endlessly decreasing sequence of reals?

The origin is at a finite location. Order starts from the bottom, if "decreasing" has any meaning.
.

Relevant Pages

  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... endlessly decreasing sequences, which TO's models require. ... Neither can the reals. ... According to TO every set of numbers has a natural order, and it is within that natural order that we must view it, but now he wants to reject the natural order because it runs counter to another of his claims. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... endlessly decreasing sequences, which TO's models require. ... Neither can the reals. ... According to TO every set of numbers has a natural order, ...
    (sci.math)
  • Re: An uncountable countable set
    ... endlessly decreasing sequences, which TO's models require. ... Neither can the reals. ... According to TO every set of numbers has a natural order, and it is within that natural order that we must view it, but now he wants to reject the natural order because it runs counter to another of his claims. ... In any case, the only way the ordinals manage to be "well ordered" is because they're defined with predecessor discontinuities at the limit ordinals, including 0. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... endlessly decreasing sequences, which TO's models require. ... Neither can the reals. ... How about the set of negative integers? ...
    (sci.math)
  • Re: An uncountable countable set
    ... endlessly decreasing sequences, which TO's models require. ... Neither can the reals. ... According to TO every set of numbers has a natural order, and it is within that natural order that we must view it, but now he wants to reject the natural order because it runs counter to another of his claims. ... I'm saying the if you iterate the negative integers starting at 0, in that order, there is no infinite descending sequence. ...
    (sci.math)