Re: Cantor Confusion

David Marcus wrote:


I suppose that depends on how you define "polygon".
Usually, a polygon
has only a finite number of vertices.

Sometimes pi is estimated by computing the circumference
of a regular convex polygon with N vertices, and letting
N->oo . But actually such a limit does not exist?



Anyway, if, for example,
you took the set of points from (0,1) excluding
the point at 1, you would not then be able to
recreate the
ordered set inclusive of the point at 1 by
re-appending it
because you would not know where to put it?

I'm sorry, but I have no clue what you mean.
Recreate? Re-append?
Wouldn't know where to put it?


All I meant was that if you have the ordered finite set
e.g. {0,1,2,3,..,N} you could partition it into exclusive subsets
{0,1,2,3,..,N-1} and {N}, and then, if you wished,
recreate the original set by appending {N} to
{0,1,2,3,..,N-1}. But when you form the open subset
of [0,1) by e.g. excluding the point {1}, you could
not form the ordered closed set [0,1] from
[0,1) and {1} - because [0,1) does not have a last member,
so you would not know where to append {1}.

---
Andy
.

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