On Fri, Mar 30, 2012 at 5:37 AM, Boyko Bantchev <boyk...@gmail.com> wrote:
>>>>>>> (f∘g)(x) ≡ f(g(x))
>> In the original definition, which led us to this point, there
>> was no statement that f and g had domains.
>
> Are there functions without domains? Since when is it customary to
> explicitly enunciate such minutiae?
Of course there are. For example, let f be a function whose
domain is the members of the empty set. J implements this ([:).
(There are also mathematical entities which are not functions,
in many branches of mathematics. Relationships have domains but
are not functions. An axiom is an example of a mathematical
entity which does not have a domain and which is not a function.
Other examples exist.)
> future I will avoid doing so. From now on, I will not comment your
> posts, and will be grateful if you do reciprocally.
I am sorry that you found this discussion disappointing, but
if you are not interested in a discussion, that's an issue
for you to deal with. I am not going to agree to take any
future steps to address the issue of what discussions you
find interesting.
That said, we got into this discussion because there is a
mismatch between the symbols as we use them in J and the
symbols as we use them in Haskell. I tried to call that
out, and you resorted to claiming that the Haskell definition
was a feature of "Mathematics" without any further qualification.
But Mathematics is a huge subject which uses many notations,
so I objected to that line of argument. [I remember one
college class I took ("Introduction to Arithmetic") where
we literally had new notation on every page of the textbook.]
Anyways, I do not have time to review every major recorded
example of mathematical notation. Nor should I need to,
even when I am calling out an ambiguous statement as
ambiguous.
--
Raul
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