To:Qfwfq and Craig D,
You know, in my previous post, I made it absolutely clear that those pesky "indeterminate forms" don't even exist if we do the algebra correctly and "cross out" the logarithms at z=1 and z=2.
In other words, the beingness of the pesky expression: (1)^(0/0) is "zip", "zero", "nada" at z=1 and z=2.
Now, if they don't exist, then they are a non-issue and we are really going off topic in discussing them!
The proof works precisely because z=1 and z=2 are the only possible values of z that allow us to "cross out" the logarithms preventing T=c.
That's all there is to it. No point in discussing "indeterminate forms" that either can, or must be "crossed out" before they even exist and are therefore perfectly consistent with the result:
(1)^(0/0)=1,
just as the "counterintuitive" expression: (p)^(0), is perfectly consistent with the result:
((p)^(q))/((p)^(q))=(p)^(q-q)=1.
Take another look at my post #60 and consider this fact: If it were not the case that the expression:
(1)^(0/0)=1,
then logarithms themselves would have to be viewed as an "inconsistent construct" because their properties would not allow T=c in (3) and (4), but would allow T=c in (5) and (6).
We would then have to banish logarithms from mathematics altogether!
Don't you see, we simply can't eliminate logarithms from mathematics, so we absolutely must conclude that:
(1)^(0/0)=1,
because it's not just the only logical and consistent conclusion, but the only possible conclusion as well! I simply can't accept your view that the properties of logarithms are somehow "bogus".
We must keep in mind that new discoveries often show us new things and therefore bring about new points of view.
I discovered "cohesive terms" about a decade ago, and showed how they are derived and defined apart from "non-cohesive terms" throughout my website. As their inventor, I had to give them a name, and chose "cohesive term" because they are the first and only algebraic terms in the history of mathematics that actually prevent cancelled factors or cancelled common factors from "falling off" and getting "lost".
I introduced them here in this forum because that property alone is nothing less than astonishing!
Now, let's get back on topic and discuss whether or not the equation:
is telling us that, in principle, multiplication and/or division by unity automatically results in division by zero.
Letting T=1 sure seems to indicate that it does!
Is this a "strange claim"?
Perhaps, but that's a good thing because in this case, it is obvious that the truth is indeed stranger than fiction!
Don
