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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: 3,551 Registered: 12/13/04
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 13, 2013 8:57 AM

On Thu, 12 Sep 2013 08:10:22 -0700 (PDT), Dan Christensen
<Dan_Christensen@sympatico.ca> wrote:

>On Thursday, September 12, 2013 10:17:54 AM UTC-4, dull...@sprynet.com wrote:
>> On Wed, 11 Sep 2013 11:25:54 -0700 (PDT), Dan Christensen
>>
>> <Dan_Christensen@sympatico.ca> wrote:
>>
>>
>>

>> >Is there a more divisive is issue in all of mathematics?
>>
>>
>>
>> Calling this a divisive issue in mathematics is utterly
>>
>> silly. It's not even an issue, much less divisive.
>>

>
>Judging by the lengthy debates in various online forums, I would say this is a divisive issue.

That's hilarious. Do you also feel that the uncountability of the
reals is a divisive issue in mathematics? Or the "question" of
whether 0.999... equals 1?

>(For example, the ongoing "Ask A Mathematician" thread on this topic starting in December 2010 now has 982 postings!)
>
>

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

There are certainly situations where it's most convenient to interpret
0^0 as one thing, and situations where it's most convenient to
iintepret it as something else. It's possible (not that I'm conceding
that) that this has some bearing on what programming languages
should do.

How in the world do you get from there to the idea that this
is "a divisive issue in mathematics"?

>Dan