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Re: 0^0=1
Posted:
May 6, 2012 1:54 PM
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LudovicoVan wrote:
>
> (I'll talk about 0/0 because 0^0 can be shown to be equivalent.)
If they're equivalent, you'll be able to repeat your argument using
0^0. Go on then.
> On the contrary, there are all reasons: in the case 0/0, that is, by
> definition of division, "the number which, when multiplied by 0, gives 0",
> and you just do not have ground to chose a specific value among all the
> possible values that would fit the bill. But the point is even more
> technical than that, as you do get to (easily) prove that 1==0 if you adopt
> any such definitions. This is how I would show it:
>
> 1
> = 1 + 1 - 1
> = 0/0 + 0/0 - 1
> = (0+0)/(0*0) - 1 -- 0/0 is defined, isn't it?
> = 0/0 - 1
> = 1 - 1
> = 0
>
> Hence please re-read what I said, because one thing is to patch a function,
> other thing is the properties of the corresponding operations and the
> manipulations you are then entitled to perform. In particular, you are
> surely entitled to take 0/0:=1 in order to attain this or that specific
> computational goal, but you have to put careful and strict limits on where
> that definition can be used, otherwise all you will get is an inconsistent
> system. And these limits are what we usually denote as "exceptions", in the
> broad sense.
>
> -LV
>
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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