Re: infinity

Randy Poe <poespam-trap@xxxxxxxxx> wrote:

> 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.

But you are forgetting that in TOmatics {2, 3, ... } is
meaningless. You have to provide an 'arbitrary largest'
element in order for it to be a proper TO-set.

So you can talk about {2, 3, ... N} and { -N, ... -2, -1, 0},
but 1 is not the "center" of those two sets. 1 is
the center of {2, 3, ... N+1} and { -N+1, ... -2, -1, 0 }.

0 may have been the center of { 1, 2, 3, ... N}
and { -N, ... -3, -2, -1}, but when you change
the center you also have to adjust your ranges.
You cannot just talk about the entire number line,
but only "finite" or "infinite" segments of it.

Stephen
.

Relevant Pages

  • Re: infinity
    ... >>> There is an infinite expanse on either side. ... >> So let -oo be the midpoint of TO's line without endpoints. ... > b) (as Tony says above), N on the left and N on the right, regardless ...
    (sci.math)
  • Re: Dialling in an amp
    ... at it but I suck. ... volume at midpoint, then twiddle from there until I get what I want. ...
    (alt.guitar)
  • Re: Well Ordering the Reals
    ... > TO has given no satisfactory reason to doubt the standard resolution. ... I think Tony is refreshing, ... Virgil basically attacks Tony, and as above tries to segregate him. ...
    (sci.math)
  • Re: infinity
    ... >>> distinct paths in the binary tree representing the binary number strings. ... whose closest common node is the root. ...
    (sci.math)
  • Re: Right or wrong?
    ... He CHOSE not to. ... your own interpretation of a much more difficult piece, IMO. ... This is not a black & white discussion as we found ourt last time ...
    (alt.guitar.beginner)