Science Forums 2

[Qfwfq]

As a mathematician, I distinguish between "conclusive arguments" and "non sequiturs". Don, I'm also beginning to see that you need to straighten out your grasp on the fundamentals of logic. Let's look at the fallacies in your argument:

Originally Posted by Don Blazys

Now, if N is a non-negative integer, then the "blunt form":

(0/0)=N

implies that any non-negative integer N multiplied by 0 equals 0.

That's a "reasonable implication" because N*0=0 is a "true statement".

Actually, it is a truism:



is formally a true implication, but only because the consequent is true and not by force of any argument; you might as well put in any satement as the implicant (even a false one!). There is circularity in attempting to argue the implication; after multiplying both sides of by zero and then applying the implicant to the resulting rhs, you could only conlclude as a consequent. At this point, in order to deduce from that, one would need to use it (i. e. already know it is true).

The trouble is that, since the argument relies on multiplying both sides by zero, even if it could fully lead to the implication (), it certainly couldn't demonstrate a co-implication (). It therefore does not justify using the true statement to justify at all. I'm under the impression you need to avoid confusion between modus ponens and modus tollens, your argument demonstrates nothing about defining any value; it is inconlusive.

The implication is also formally a true one, what can you deduce from it?

Originally Posted by Don Blazys

because N*0=6 is a "false statement".

Of course it is a false satement and I already said so, so we need not even consider it. Friday I left out that a fair comparison would be one between:

and

where both equalities may be seen as possibly resulting from true limits, by replacement of infinitesimal terms with blunt zeroes. What I meant Friday by "sleight of hand" is that your comparison wasn't a fair one; it's blithering obvious that can't be similarly obtained.

Originally Posted by Don Blazys

Please keep in mind that indeterminate forms such as (0/0) are often initially encountered in their "blunt forms", and that in some cases (such as my proof), they should remain that way, while in other cases, they should be evaluated by introducing more subtle concepts such as limits.

I should keep what in mind? You appear not to have understood what I posted on Friday; I was talking about limits, wasn't I? My point was indeed that these things make sense only in the context of computing limits, with the zeroes actually being infinitesimals! Try not to miss my points if you reply to them.