From: Rupert S. <rsw...@gm...> - 2014-03-24 22:20:11
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Bill Wood <wil...@co...> writes: > But we have to be careful in mathematical contexts. I can say that the > Collatz function, defined in maxima by > > (%i1) C(n) := if evenp(n) then n/2 else 3*n+1; > > has an *integer* domain but if I say it has an *integral* domain > mathematicians would say I spoke badly or even nonsensically since an > integral domain is an algebraic structure (a commutative ring with unity > 1 /= 0 with no zero divisors). Note that the rationals, the reals and > the complexes all form integral domains. When restricting attention to > the integers I would prefer to use "integer" over "integral" even at the > expense of linguistic grace. Of course that's just me. Indeed, but I'm not convinced that C(n) has an "integer domain". To me, its domain is "the integers". Saying that it has "an integer domain" or "an integral domain" (forgetting my commutative algebra for a second), makes me think that its domain is an integer, which is clearly wrong... Anyway, I'll stop nit-picking now, because the yak is well and truly hairless... Rupert |