Re: infinity

*** T. Winter said:
> It started all with:
> > No I defined infinite nubmbers in terms of finites and zero. I have
> > posted that definition at least eight times.
> Next we go along quite a few definitions and now we are stuck at the
> definition of infinitesimals.
Multiplicative inverses of the infinites?
>
> In article <MPG.1da33b0fd8f73da998a387@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow <aeo6@xxxxxxxxxxx> writes:
> > *** T. Winter said:
> > > No. How do you define the real number line, and the term "a finite points
> > > away"?
> >
> > I defined finite number. The number of points between a number and another
> > number may be finite or infinite. If it is zero, they are the same number.
> > Any finite number is an infinite number of points from zero. An
> > infinitesimal is a finite number of points from zero.
>
> As I still do not know how you define "the real number line" I am still stuck.
> Off-hand I would say that if the real number line consists of a discrete
> set of points we can talk about a finite number of points away (and in my
> understanding *all* points are a finite number of points away). On the
> other hand, if it is a continuous set of points, I have no idea what to
> do with the term "a finite number of points away".
Are you saying that there are a finite number of points between 0 and 1? They
seem like an infinite number of points from each other, to me. When you say a
"continuous set of points" it sounds almost oxymoronic. Either it is some kind
of continuous line, or it is a set of points. This is one area where Lester and
Albert come to blows. Albert can't see a line being made up of points but as
being deifned by two points, while Lester sees points as isolated nothings
which are only identified as the intersection of lines which determine the
space in general, which perspective I can see. I think things can be viewed
both ways. When it comes to picturing the line on a infinitesimal scale, I
believe it may be helpful to imagine those points as being connected by
infinitesimal line segments that connect immediately neighboring points. In
this sense the continuum can be viewed discreterly as a linked list, which is a
tree where each node has one child. The nodes become the points, and the
branches become the line segments that connect the points. If you declare these
infintiesimal line segments to be your unit infinitesimal, does that mean there
can be nothing smaller? Not at all. There are certainly infinities larger than
the unit infinity, and there are corresponding infinitesimals for every
infinity (more or less - there may be some computational issues, I imagine, in
cases).
>
> I would think that if number 'a' is one point away that a/2 does not exist.
> So what is that mysterious a?
Unit infinitesimal, 0.000...001. a/2 is going to be half that, or N/2 second
order infinitesimals, 0.000...000:500...000. See how easy it is?
>
> > > > Yes i know: "undefined".
> > > > > The standard definition of inverse reads: the inverse of a number a
> > > > > is a number b such that a * b = 1. The inverse is noted as a^(-1),
> > > > > or also as 1/a. Now what is your definition of the "inverse" of 0?
> > > >
> > > > oo
> > >
> > > So 0 * oo = 1? If not, what is your general definition of inverse?
> >
> > Yes, for unit oo and 0, oo*0=1.
>
> Again some undefined term. "unit".
You do not know what a unit of measure is? An arbitrary value used as a measure
for the purpose of calculating and comparing values.
>

--
Smiles,

Tony
.

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