Re: Cantor Confusion

On 12/1/2006 8:55 PM, Virgil wrote:
In article <45700723.3060406@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

On 11/30/2006 1:39 PM, Bob Kolker wrote:

Division by zero in a field yeilds a contradiction.

Just this contradiction resides already in the notion of (actual)
infinity.


Division by zero in standard sets of numbers is not defined because
there is never a unique x in such sets of numbers for which a = 0*x.
Either no x works or more than one works.

Infinity has nothing to do with it.

A finite example:

The residues of the integers modulus a prime is always a finite field
under the usual addition and multiplication, so there is no
"infinity" involved, but division by zero in those fields is still
barred for the reason above, a = 0*x can never have a unique solution.

I do not feel limited in thinking to the indefinitely large. I likewise
consider the indefinitely small (infinitesimal).


Isn't it better to understand why it is incorrect than simply to learn
it is forbidden?

Eckard Blumschein

It is better to understand the real reason (see above), but Eckard
doesn't seem to understand the real reason. It has nothing to do with
"infinity".

Not directly with the indefinitely large, yes.


.

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