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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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 Michael F. Stemper Posts: 125 Registered: 9/5/13
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 13, 2013 9:28 AM

On 09/13/2013 07:57 AM, dullrich@sprynet.com wrote:
> 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?

(The "issue" is
<https://cs.uwaterloo.ca/~alopez-o/math-faq/node40.html#SECTION00530000000000000000>.)

>>> 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?

The latter was the example of a non-issue that came to my mind, as well.

>>> 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?

How about the context of making the medical equipment work properly?

>> 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"?

Teach the controversy!!!

--
Michael F. Stemper
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