Re: infinity


David R Tribble wrote:
> Tony Orlow wrote:
> >> Who said anything about endpoints. It's any point on the line, which acts
> >> as the center for the infinite expanse.
> >
>
> Randy Poe said:
> >> So any point on an infinite line is a center of the line,
> >> meaning there is just as much line to the right as to the left?
> >
>
> Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> >> There is an infinite expanse on either side.
> >
>
> Virgil wrote:
> > TO's "line", supposedly without endpoints, was given by TO as [-oo,+oo].
> > TO says one may chose any point on the line as midpoint.
> > So let -oo be the midpoint of TO's line without endpoints.
>
> Similarly, I would propose that if there are 'N' points to the right
> of zero (Tony's 'N', or his 1:000...000), and 'N' points to the left
> of zero, then choosing, say, +N/2 as the midpoint should leave either
> a) 3N/2 points to the left and N/2 points to the right, or
> b) (as Tony says above), N on the left and N on the right, regardless
> of the midpoint. Which answer would Tony choose?

I await the answer with baited breath (misspelling deliberate).

I was leading up to a more modest question, which is that
Tony's new claim seems to imply that since +1 is a center point,
the number of naturals in {2, 3, ...} is the same as in
{..., -2, -1, 0}. While all of us agree with this, it would
seem to contradict an early axiom of TOmatics.

- Randy

.

Relevant Pages

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    ... Tony Orlow wrote: ... >> There is an infinite expanse on either side. ... > So let -oo be the midpoint of TO's line without endpoints. ...
    (sci.math)
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  • Re: infinity
    ... >> Virgil wrote: ... >>> TO says one may chose any point on the line as midpoint. ... >> b) (as Tony says above), N on the left and N on the right, regardless ...
    (sci.math)