Re: Cantor Confusion



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


Large enough is certainly not qualitatively different enough, infinity
is the location where two parallel lines are thought to meet each other,
and division by zero has been forbidden because it yields anything.

Division by zero in a field yeilds a contradiction.

Just this contradiction resides already in the notion of (actual)
infinity. The task division by zero cannot be performed. It would
require to leave the realm of numbers.


1/0 = x (for some x in the field) implies 1 = 0*x = 0. That simply will
not do.

Likewise oo + a = oo seems to imply a = oo - oo = 0.

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

Eckard Blumschein

.

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