Re: Infinite
- From: "Ross A. Finlayson" <raf@xxxxxxxxxxxxxxx>
- Date: 29 Apr 2005 20:01:02 -0700
Virgil wrote:
> In article <1114820149.537062.271510@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> "ligriv" <vbgtpublios@xxxxxxxxx> wrote:
>
> > is a ray more infinite than a line?
>
> If anything, less. A line has no endpoints but a ray has one.
>
> But strictly in terms of cardinality, no.
You mean the set of points comprising that line right?
That is, the set of points where each point is on that ray or line and
everywhere and everywhere on that ray or line is a point, due to the
completenesss/gaplessness of the reals in their continuity on the line,
ray, or line segment?
Are you talking about what may be considered a _sequence_ of those
points? Alternatively, they may not be well-ordered, because of one of
apparently your favorite mathematician's, Cantor's, "first proof of the
uncountability of the reals", variously known in these parts as "nested
intervals" or sometimes Cantor/Megill.
Induction is infinite.
Virgil, yes and no.
In one sense, there are twice as many points on the line as the ray,
for the origin is everywhere. In another, they are the same, for the
same reason.
One of the problems with deep foundations is that so many things become
trivially true that it is difficult to separate them, in a technical
sense.
This is where recently I have decided to call the stuff between
first-order predicate logic and set theory "deep foundations",
Platonistically, formally, intuitionistically, etcetera. That is to
say, basically, deep foundations of the philosophy of the mathematical
logic, towards the strong, consistent, complete, and concrete theory.
The particle is: point, and wave.
Ross
.
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