Re: An uncountable countable set

In article <454973f1@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Mike Kelly wrote:
Tony Orlow wrote:
stephen@xxxxxxxxxx wrote:
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
stephen@xxxxxxxxxx wrote:
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
stephen@xxxxxxxxxx wrote:
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
stephen@xxxxxxxxxx wrote:
<snip>

What does that have to do with the sets IN and OUT? IN and OUT are
the same set. You claimed I was losing the "formulaic
relationship"
between the sets. So I still do not know what you meant by that
statement. Once again
IN = { n | -1/(2^(floor(n/10))) < 0 }
OUT = { n | -1/(2^n) < 0 }

I mean the formula relating the number In to the number OUT for any
n.
That is given by out(in) = in/10.
What number IN? There is one set named IN, and one set named OUT.
There is no number IN. I have no idea what you think out(in) is
supposed to be. OUT and IN are sets, not functions.

OH. So, sets don't have sizes which are numbers, at least at
particular
moments. I see....
If that is what you meant, then you should have said that.
And technically speaking, sets do not have sizes which are numbers,
unless by "size" you mean cardinality, and by "number" you include
transfinite cardinals.
So, cardinality is the only definition of set size which you will
consider.....your loss.
If somebody presents another definition of set size, I will
consider it. You have not presented such a definition.


I have presented an approach that works for the majority of infinite
bijections, and explained some of the exceptions. IFR works for all
numeric sets mapped from a common set. N=S^L works for all languages,
including those that express the first set. Both work on a parameteric
basis, using infinite case induction to finely order the values of
formulas for a specific infinite n. Rare exceptions include the set 1/n
for neN, whose inverse is itself, which IFR ends up saying has size 1,
but that's because the natural indexes and fractional mapped reals only
share one point in their range, 1. So, I think Bigulosity is worth
considering.

Why? What is it good for? What theories is it used in?


Bigulosity Theory.

Something that exists only in TO's dream world, is of no use anywhere
else and of little use there except as a diversionary tactic. TO only
brings it up when he his backed into corners.
.

Relevant Pages

  • Re: An uncountable countable set
    ... You claimed I was losing the "formulaic relationship" ... I have presented an approach that works for the majority of infinite ... IFR works for all ... Rare exceptions include the set 1/n ...
    (sci.math)
  • Re: An uncountable countable set
    ... You claimed I was losing the "formulaic relationship" ... I have presented an approach that works for the majority of infinite ... IFR works for all ... Rare exceptions include the set 1/n ...
    (sci.math)
  • Re: infinity
    ... that does not make him a crank. ... >> the concern of Russell, and Ord, Burali-Forti, a paradox in ZF. ... >> Hoyle, transfinite cardinals aren't useful. ... >> Infinite sets are infinite. ...
    (sci.math)
  • Re: A puzzle for Cantorists
    ... trichotomous in the infinite, for example. ... Trichotomy, which says that for all x and y in the cardinals, either x ... Trichotomy amongst transfinite cardinals, ...
    (sci.math)
  • Re: infinity
    ... The universe is infinite, infinite sets are equivalent. ... Basically, axiomatization leads to incompleteness, so then the idea is ... hold, and non-measurable sets don't exist, and transfinite cardinals ...
    (sci.math)