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Topic: Formal proof of the ambiguity of 0^0
Replies: 6   Last Post: Nov 17, 2013 2:04 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: Formal proof of the ambiguity of 0^0
Posted: Nov 17, 2013 10:19 AM
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"Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message
news:90552961-bcc8-40d8-856a-6cbc94d8c52c@googlegroups.com...
> On Saturday, November 16, 2013 12:41:35 PM UTC-5, Bart Goddard wrote:
<snip>
>> (We'll leave aside the incorrect assumption that leaving
>> 0^0 undefined is "common practice.")

>
> Every high school graduate knows that 0^0 is undefined, but not
> necessarily why this is so.


We were simply explained that 0^0 = 0/0, because x^0 = x/x when extending
the notion of repeated multiplication to non-positive exponents. Indeed,
your rationale for leaving 0^0 undefined isn't different from the one for
0/0, that "every number works": a high school rationale at best.

> Using my approach, it will now be easy to make the case rigorously using
> only basic arithmetic. Not everyone will get it (you, for example, Barty),
> but I think most will get it right away and wonder what all the fuss was
> about.


It is you who keep missing the point: we are not allowed to divide by zero
in high school either, yet functions get extended all the time.

Julio





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