On 14/10/2019 18:25, Andrew Barnert via Python-ideas wrote:
On Oct 14, 2019, at 01:53, Chris Angelico<ros...@gmail.com> wrote:
On Mon, Oct 14, 2019 at 7:04 PM Andrew Barnert<abarn...@yahoo.com> wrote:
If you’re wondering whether integers are something you could define the laws of
complex algebra over, then no, it isn’t. For example, one of the laws is that
every number besides 0 has a multiplicative inverse, which obviously isn’t true
for the set of integers. Or for the set of Python `int` values. But that’s not
what the ABC is testing for, so that’s fine.
Hmm, but every nonzero integer DOES have a multiplicative inverse -
that value isn't another integer, but there is one.
Sure, you can define a function from integers to rationals, but that isn’t a
function from integers to integers, so that doesn’t make integers a field. To
define a group/ring/field/algebra/etc. you need operations from that object to
itself. Those operations are part of the definition of the object. And the
rules that distinguish what object counts as a field, or as a division ring,
etc. are rules on the operations used to define it.
Speaking as someone with a dusty maths degree, can I just say that you
are massively missing the point here? There exists an injection from
integers to complex numbers, that's all that anyone has actually claimed
here. You seem to be basing your entire contradiction on the
informality of the notation they used. That's really not useful, nor is
it meaningfully contributing to the original discussion.
Can we get back to the original point, whatever that was?
--
Rhodri James *-* Kynesim Ltd
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