On 9/20/2011 19:16, clipka wrote:
> Also it was not invented because someone thought that some mathematical
> operations were "somehow impure", but to systematically prove some
> assumptions that had simply been taken for granted in earlier mathematical
> work.

OK. I had been taught that the whole concept of "limits" was invented 
because while there was a working set of math that involved calculating 
stuff about 0/0 for example, it wasn't really quite right.

> Besides, there is no such thing in (modern day) mathematics as "somehow
> impure";

Of course. But the guy who invented calculus is the same guy who specified 
that things are "defined" and "undefined" and "proven" and "unproven." :-) I 
wasn't talking about modern math, obviously.

> And x=1/0 /is/ undefined on the set of real (or complex)
> numbers, because there is no solution to x*0=1 in that domain.
>

Sure. Never argued against that.

> For any domain that includes an element inf:=1/0 satisfying inf*0=1, each
> and every mathematical property of the body of real (or complex) numbers
> must be re-evaluated with respect to this new element inf, and exceptions
> need to be established for various mathematical operations. For instance, if
> you want inf to have the property that inf+x=inf for x!=0, you'll obviously
> need to break even such simple properties as y+x=y <=> x=0.

Yep.

-- 
Darren New, San Diego CA, USA (PST)
   How come I never get only one kudo?

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