Re: Is a line segment composed of points?

On Nov 12, 1:02 am, Venkat Reddy <vred...@xxxxxxxxx> wrote:

You seem to be indicating the following -

1. There is a single number which can be called as "infinitely small"
number. Lets call this as epsilon.
2. The epsilon is a result of a set of cuts but not just two cuts
unlike other non-zero pieces.
3. The extent of epsilon is zero but we also call it "infinitesimal"
or infinitely small number.

First of all, we need not restrict infinitely small numbers to a
single number, just as we don't restrict infinite to a single largest
number. Secondly, a line segment can only be a result of two cuts, but
not a result of a set of cuts by any conceivable logic. And finally,
we still don't have a reason why an infinitely small number should be
equal to zero.



Basically no. I do not claim that
an infinitely small number must be zero. I
claim that the extent of the first piece is zero,
but it is only you that claims the extent of the
first piece is an infinitely small number.

Things we agree on:

1. There are an infinite number of
infinitely small numbers. None of these
is zero.

2. If we cut the line segment [0,1] at every
point 1/N, we are left with a piece which has
an endpoint 0. We can describe this
piece as [0,b]

Things we do not agree on

1. My claim is that b is 0. Your claim is that
b is not zero but infinitesimal.

2. My claim is that b is not defined by any one
cut. Your claim is that any line segment,
[and hence [0,b] and hence b ] is defined by
one (two?) cuts.

My questions are:

Given that there are an infinite number of
infintesimals, how do we determine which of
these is b?

Given that there are an infinite number of cuts,
how do we choose one cut to define b?



- William Hughes


.

Relevant Pages

  • Re: Is a line segment composed of points?
    ... piece if of zero length, then it is not a result of cutting at ... You end up with an infinite number of pieces, ... segment is a matter of how you define line segment. ... first segment is not reached by a division process. ...
    (sci.math)
  • Re: Is a line segment composed of points?
    ... piece if of zero length, then it is not a result of cutting at ... You end up with an infinite number of pieces, ... segment is a matter of how you define line segment. ... first segment is not reached by a division process. ...
    (sci.math)
  • Re: Is a line segment composed of points?
    ... piece if of zero length, then it is not a result of cutting at ... You end up with an infinite number of pieces, ... segment is a matter of how you define line segment. ... Cutting a line segment at its non-boundary points is a division ...
    (sci.math)
  • Re: How Many Of You Had To Teach Yourself The Math?
    ... using derivatives. ... bottom lid) and body cylinder itself that must be made out of the ... this point, we have two variables, H and D, and there are an infinite ... One where the area of the lids is about zero and the ...
    (sci.electronics.basics)
  • Re: TM Tape is Always Finite
    ... process to be repeated an infinite number of times; ... mental model of infinity, and has tripped you up at least ... one that holds for that zero for all time. ... > to assume that TM2 can as well. ...
    (comp.theory)