Quote:
Originally Posted by Don Blazys
...there are plenty of cases, contexts and circumstances in which equations such as:
(0/0)=1 can be viewed as "meaningfull". (Especially in the context of "limits".)
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Gosh Don, I was talking about the blunt
form and I said so. I was distinguishing it from limits of any kind of expressions in the exponent.
In terms of limits, it is clear that the ratio of two
infinitesimals (a distinct thing from the ratio of 0 and 0), can have a limit of any value (according to what the two infinitesimals are). It is also trivial to argue that
any limit of:
exists and can only be equal to 1. By "any limit of" I mean the limit for x approaching any accumulation point of the domain of
.
has no domain, no accumulation points, it cannot have any limit. It simply does not and cannot define any value (for any value of
or any other variable).
Do you understand the distinction Don?
Quote:
Originally Posted by Don Blazys
There are, however, no conditions under which equations such as:
(6/0)= N can be construed as meaningfull, so the expressions:
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Obviously, if by N you mean a finite value! (or an infinitesimal one) You attempted a sleight of hand here!
Quote:
Originally Posted by Don Blazys
Also, (0/0)= (infinity) if and only if (infinity)*0=0. (Again, the meaning/value of (0/0) depends entirely on the context in which it occured.)
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This gets you into the same paralogism I had already pointed out.
Quote:
Originally Posted by Don Blazys
I suppose that different mathematicians have different criteria for what constitutes a "valid result". For me (and most mathematicians my age), those criteria are "consistency" and "beauty".
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This is a very dubious statement, self-consistence is a criterion of validity, but beauty is not.
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Inutil insegnà al mus, si piart timp, in plui si infastidìs la bestie.
Hypography Forum PITA...... er, Administrator.
