On Friday, November 1, 2013 10:02:55 AM UTC-4, Bart Goddard wrote: > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:13a5c4b5- > > email@example.com: > > > > > Again, 0^0 is a natural number, but no value is assigned to it > > > > And you don't see this as a problem? You don't realize > > that (here) "assigning" and "defining" are synonyms? >
You are a slave to convention. This issue really calls for some thinking "outside the box." As readers here may recall, I myself relented for a day or two after first proposing this idea. It just seemed too weird. But as I recently read on one of those pithy billboards in NYC, "It's only weird if it doesn't work!" And much to my amazement, it DOES work really quite well.
You yourself have admitted that 0^0 is ambiguous. How do YOU propose to formalize this ambiguity, keeping in mind that in a formal proof, you can only construct power sets, Cartesian products and subsets from other sets? You can't just pull functions out the air. You must construct an appropriate set of ordered triples (in this case), prove it is a function and establish its essential properties that you might use as its "definition."
> To be logical, you're going to have to choose between > > the assertions: 1. 0^0 is undefined and 2. 0^0 has > > a numerical value. >