HaloO,
Larry Wall wrote:
Then [X]() also is ()? How about (0,1) X ([]) === (0,1)?
No, that's (0,[]), (1,[1]). [] *doesn't* flatten in list context.
I guess you meant (0,[]), (1,[]). And you didn't answer what
[X]() returns. Following your arguments this would be undef.
I am genuinely
On Apr 12, 2008, at 17:37 , Moritz Lenz wrote:
[EMAIL PROTECTED] wrote:
Technically the Cartesian cross operator doesn't have an identity
value.
It has.
The set which contains only the emty set, or in perl terms ([]);
If (a, b) denotes an ordered pair you get
{0, 1} X {{}} = {(0, {}),
-Original Message-
From: Mark A. Biggar [mailto:[EMAIL PROTECTED]
Sent: Sunday, April 13, 2008 11:22 PM
To: Miller, Hugh
Cc: Moritz Lenz; p6l
Subject: Re: cross operator and empty list
Miller, Hugh wrote:
From: Moritz Lenz [mailto:[EMAIL PROTECTED]
[EMAIL PROTECTED] wrote
On Apr 14, 2008, at 12:05 , TSa wrote:
HaloO,
Xavier Noria wrote:
{0, 1} X {{}} = {(0, {}), (1, {})}
which, you see, is different from {0, 1}. They have different
elements. The fact that there's a clear mapping that sort of
identifies them has nothing to do with set equality.
But X is
HaloO,
Xavier Noria wrote:
{0, 1} X {{}} = {(0, {}), (1, {})}
which, you see, is different from {0, 1}. They have different elements.
The fact that there's a clear mapping that sort of identifies them has
nothing to do with set equality.
But X is cooperating with , in Perl 6:
(0,1) X
On Mon, Apr 14, 2008 at 12:05:15PM +0200, TSa wrote:
But X is cooperating with , in Perl 6:
(0,1) X (()) === ((0,()),(1,())) === (0,1)
That is, X strips the outer list and comma concatenates the
inner empty list away.
No, the inner () is also in list context, and () in list context
always
HaloO,
Larry Wall wrote:
No, the inner () is also in list context, and () in list context
always just disappears.
And 0,1 X () is going to be (). Perl 6's infix:X is defined over
lists, not sets. If you want to overload X for set types, you may.
Then [X]() also is ()? How about (0,1) X
HaloO,
I wrote:
Then [X]() also is ()? How about (0,1) X ([]) === (0,1)?
The original question was sort of about how to write a list
that has .elems == 1 but no content.
Other ideas are: [[]] and @@() with the latter not very likely
because it implies any multidimensional array somehow having
On Mon, Apr 14, 2008 at 06:28:06PM +0200, TSa wrote:
HaloO,
Larry Wall wrote:
No, the inner () is also in list context, and () in list context
always just disappears.
And 0,1 X () is going to be (). Perl 6's infix:X is defined over
lists, not sets. If you want to overload X for set
On Mon, Apr 14, 2008 at 06:28:06PM +0200, TSa wrote:
The original question was sort of about how to write a list
that has .elems == 1 but no content.
Wouldn't that just be [[]] ?
Mark J. Reed [EMAIL PROTECTED]
At 09:58 -0700 4/14/08, Larry Wall wrote:
By the way, you don't need to put parens around the arguments to X. It takes a
list on either side. We made it tall so that it would stand out visually
anyway:
$a,$b,$c X $x,$y,$z
How long before some engineer or 3D graphic artist gets really
On Mon, Apr 14, 2008 at 11:47:04AM -0600, Doug McNutt wrote:
: At 09:58 -0700 4/14/08, Larry Wall wrote:
: By the way, you don't need to put parens around the arguments to X. It takes
a list on either side. We made it tall so that it would stand out visually
anyway:
:
: $a,$b,$c X $x,$y,$z
Doug McNutt douglist-at-macnauchtan.com |Perl 6| wrote:
At 09:58 -0700 4/14/08, Larry Wall wrote:
By the way, you don't need to put parens around the arguments to X. It takes a
list on either side. We made it tall so that it would stand out visually
anyway:
$a,$b,$c X $x,$y,$z
-Original Message-
From: Moritz Lenz [mailto:[EMAIL PROTECTED]
Sent: Saturday, April 12, 2008 10:37 AM
To: [EMAIL PROTECTED]
Cc: p6l
Subject: Re: cross operator and empty list
[EMAIL PROTECTED] wrote:
Technically the Cartesian cross operator doesn't have an
identity value.
It has
Miller, Hugh wrote:
From: Moritz Lenz [mailto:[EMAIL PROTECTED]
[EMAIL PROTECTED] wrote:
Technically the Cartesian cross operator doesn't have an
identity value.
It has.
The set which contains only the emty set, or in perl terms ([]);
Or am I missing something?
Should be a (any) 1 point set
[EMAIL PROTECTED] wrote:
Technically the Cartesian cross operator doesn't have an identity value.
It has.
The set which contains only the emty set, or in perl terms ([]);
Or am I missing something?
Cheers,
Moritz
--
Moritz Lenz
http://moritz.faui2k3.org/ | http://perl-6.de/
signature.asc
HaloO,
Larry Wall wrote:
(@a X @b X @c).elems == @a.elems * @b.elems * @c.elems
Sorry, I was aiming at defining a neutral element of the X
operator. In cartesian products of sets this is achieved
by having a set that contains as sole member the empty tuple.
So how would that be written?
On Mon, Apr 7, 2008 at 4:50 AM, TSa [EMAIL PROTECTED] wrote:
HaloO,
Larry Wall wrote:
(@a X @b X @c).elems == @a.elems * @b.elems * @c.elems
Sorry, I was aiming at defining a neutral element of the X
operator.
A neutral element for the cross operator seems weird if that is to be
Adriano, I think perhaps what Tsa is trying to get at is the identity value
for the X operator, and I believe I know what it is.
In the relational model of data, both the version of the model where tuples
have unordered named attributes/elements (which I prefer), and the version
where tuples
Technically the Cartesian cross operator doesn't have an identity value. There
is no set X such that
A x X = A. Now any singleton set gives a result that is naturally isomorphic
to the original set, I.e, there is a obvious bijection between the two sets,
but they are not equal sets.
--
Mark
[EMAIL PROTECTED] wrote:
Technically the Cartesian cross operator doesn't have an identity value. There is no set X such that
A x X = A. Now any singleton set gives a result that is naturally isomorphic to the original set, I.e, there is a obvious bijection between the two sets, but they are
HaloO,
why is (1,2,3) X () defined to be the empty list
and not (1,2,3) as is the case with the cartesian
product of sets which X basically is with preserved
order.
Regards, TSa.
--
The Angel of Geometry and the Devil of Algebra fight for the soul
of any mathematical being. -- Attributed to
Cartesain product with the empty set is empty. A x B is the set of all pairs
(a,b) where a is in A and b is in B. If either is empty then there are no such
pairs and the result is also empty.
--
Mark Biggar
[EMAIL PROTECTED]
[EMAIL PROTECTED]
[EMAIL PROTECTED]
-- Original message
On Fri, Apr 04, 2008 at 06:51:20PM +0200, TSa wrote:
HaloO,
why is (1,2,3) X () defined to be the empty list
and not (1,2,3) as is the case with the cartesian
product of sets which X basically is with preserved
order.
(@a X @b X @c).elems == @a.elems * @b.elems * @c.elems
Larry
Cartesian product of anything with the empty set is empty. Which is
why SQL has outer joins.
On 4/4/08, TSa [EMAIL PROTECTED] wrote:
HaloO,
why is (1,2,3) X () defined to be the empty list
and not (1,2,3) as is the case with the cartesian
product of sets which X basically is with preserved
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