[M3devel] set relationships?

Thu Apr 10 12:41:12 CEST 2008

I think the point is, <= for sets, in the form you describe,
defines a partial order.  There are libraries full of math books
describing what you can and can't do with partial orders.

And yes all your examples should be all false.

     Mika

Jay writes:
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>oops -- I mean they are all false.
>
>
>From: jayk123 at hotmail.comTo: m3devel at elegosoft.comDate: Mon, 7 Apr 2008 00:=
>38:01 +0000Subject: [M3devel] set relationships?
>
>
>I'm looking at test p1\p155.I haven't started debugging it, just trying to =
>understand it. C:\dev2\cm3\doc\reference\relations.html:"     infix    <=3D=
>, >=3D  ... (x,y: Set)     : BOOLEAN ... <=3D returns TRUE if every element=
> of x is an element of y....The expression x >=3D y is equivalent to y <=3D=
> x. ...In all cases, x < y means (x <=3D y) AND (x # y), and x > y means y =
>< x" Let's just use the sets {1} and {2}.   {1} <=3D {2}   {2} <=3D {1}   {=
>1} < {2}   {2} < {1}   {1} >=3D {2}   {2} >=3D {1}   {1} > {2}   {2} > {1} =
> All these expressions are true from the definitions above.Is that reasonab=
>le?It seems a little strange to me. I guess I am very used to strongly orde=
>red things, such that a <=3D b && a =3D> b implies a =3D=3D b, not true her=
>e, and you can't have both a < b and b < a, which you have here, and that (=
>a < b) =3D=3D !(a >=3D b) and similar, which is not true here. In this case=
>, every relation but equality is true.  - Jay=
>
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><body class=3D'hmmessage'>oops -- I mean they are all false.<BR><BR><BR>
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>From: jayk123 at hotmail.com<BR>To: m3devel at elegosoft.com<BR>Date: Mon, 7 Apr =
>2008 00:38:01 +0000<BR>Subject: [M3devel] set relationships?<BR><BR>
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>I'm looking at test p1\p155.<BR>I haven't started debugging it, just trying=
> to understand it.<BR> <BR>C:\dev2\cm3\doc\reference\relations.html:<B=
>R>"<BR><A target=3D_blank name=3Didx.194>     infix&nbs=
>p;   <=3D, >=3D  ...</A> <BR>(x,y: Set) &nbs=
>p;   : BOOLEAN<BR><BR> <BR>... <TT><=3D</TT> returns=
> <TT>TRUE</TT> if every element of <TT>x</TT> is an element of <TT>y</TT>.<=
>BR>...<BR>The expression <TT>x >=3D y</TT> is equivalent to <TT>y <=
>=3D x</TT>. <BR>...<BR>In all cases, <TT>x < y</TT> means <TT>(x <=3D=
> y) AND (x # y)</TT>, and <TT>x > y</TT> means <TT>y < x</TT><BR><TT>=
></TT>"<BR> <BR>Let's just use the sets {1} and {2}.<BR> <BR>&nbsp=
>; {1} <=3D {2} <BR>  {2} <=3D {1} <BR>  {1} < {2} <BR>&n=
>bsp; {2} < {1} <BR>  {1} >=3D {2} <BR>  {2} >=
>=3D {1} <BR>  {1} > {2} <BR>  {2} > {1} <BR>&nbsp=
>;<BR>All these expressions are true from the definitions above.<BR>Is that =
>reasonable?<BR>It seems a little strange to me.<BR> <BR>I guess I am v=
>ery used to strongly ordered things, such that a <=3D b && a =3D=
>> b implies a =3D=3D b, not true here, and you can't have both=
> a < b and b < a, which you have here, and that (a < b) =3D=3D !(a=
> >=3D b) and similar, which is not true here. In this case, every relati=
>on but equality is true.<BR> <BR> - Jay<BR><BR></BLOCKQUOTE></bod=
>y>
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>
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