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Topic: Leaving 0^0 undefined -- A number-theoretic rationale
Replies: 48   Last Post: Sep 15, 2013 1:06 PM

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 David C. Ullrich Posts: 3,555 Registered: 12/13/04
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 13, 2013 8:59 AM

On Thu, 12 Sep 2013 09:06:46 -0700 (PDT), Dan Christensen
<Dan_Christensen@sympatico.ca> wrote:

>
>> > Judging by the lengthy debates in various online forums, I would say
>>
>> > this is a divisive issue. (For example, the ongoing "Ask A
>>
>> > Mathematician" thread on this topic starting in December 2010 now has
>>
>> > 982 postings!)
>>
>>
>>
>> Ha ha. Are you claiming that an issue (whatever that means, is it
>>
>> something like a problem?) that is divisive online must be so in
>>
>> mathematics as well? Why?
>>

>
>Now, you are being silly.

_He_'s being silly? It's you who's citing those online
threads as evidence that this is "a divisive issue in
mathematics".

>
>> >
>>
>> >>
>>
>> >>
>>
>> >> In any given context we use the definition that we
>>
>> >>
>>
>> >> want to use in that context. No problem.
>>
>> >>
>>
>> >
>>
>> > What "context" is a computer programmer to use when writing software
>>
>> > for, say, medical equipment? Should he/she just assume 0^0=1?
>>
>> > Shockingly, most programming languages seem to automatically make
>>
>> > this assumption!
>>
>>
>>
>> I've told you: the programmer should do what the specification says.
>>

>
>Then what "context" is the writer of the specification supposed to use?
>
>

>> Nor is doing mathematics the same as programming computers.
>>

>
>Yeah, computers don't recognize any kind of hand-waving.
>
>

>>
>>

>> > There is a good case to be made that 0^0 is ambiguous even in the
>>
>> > natural numbers.
>>
>>
>>
>> Make it then.
>>

>
>See above.
>

>>
>>

>> > Therefore, it seems to me that the safest, most
>>
>> > conservative assumption when programming is that 0^0 should be
>>
>> > flagged as an error condition. This should be a global standard built
>>
>> > into every general purpose programming language.
>>
>>
>>
>> Yet again confusing mathematics with programming.
>>

>
>Just pointing out the obvious overlap.
>
>Dan