Re: infinity

Randy Poe said:
>
> Tony Orlow wrote:
> > Randy Poe said:
> > >
> > > Tony Orlow wrote:
> > > > Daryl McCullough said:
> > > > > >> That's provably false. Consider the set of all real numbers
> > > > > >> x such that 0 < x < 1. The range is 1, but 1 is not an element
> > > > > >> of the set.
> > > > > >
> > > > > >The range is <1, as I have said repeatedly
> > > > >
> > > > > That isn't a number, so it isn't an element of the set { x | 0 < x < 1 }.
> > > > I never said the range had to be an element of any arbitrary set.
> > >
> > > Doesn't it have to be a number? What kind of thing is "<1"?
> > >
> > >
> > It's a range of numbers.
>
> So the range of a set can itself be a set. But WHAT set?
>
> That's odd.
>
> > Perhaps, when there IS a max and min, I should state
> > the range as <=x,
>
> That's not a number either. Or a set. What values are
> in the set "<1" or the set "<=1"? Do you mean all numbers
> less than (or equal to) 1? Is -17000 in those sets?
Differences range from 0, the difference between any value and itself, and up.
There is no need to specify this lower bound on differences. What is a negative
difference?
>
> > so that the range of values in [0,1] is <=1. Does that make
> > it clearer?
>
> No, since you are still using an undefined notation. If this
> is a set, I have no way to tell what elements are in the set.
In that set of reals, all values x st 0<=x<=1.
>
> > All differences are less than or equal to 1. In {0,1) all
> > differences are less than 1. In the finites, all differences are less than oo.
>
> So the range of every set is the set itself? That seems a
> little redundant.
No, the range, say, of [15,20) is <5. Those other two examples start from the
smallest possible quantities, so it seemed like you said, but clearly is not.
>
> - Randy
>
>

--
Smiles,

Tony
.

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