[M3devel] set relationships?

[Jay]

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    <=, >=  ... 
(x,y: Set)     : BOOLEAN
 
... <= returns TRUE if every element of x is an element of y.
...
The expression x >= y is equivalent to y <= x. 
...
In all cases, x < y means (x <= y) AND (x # y), and x > y means y < x
"
 
Let's just use the sets {1} and {2}.
 
  {1} <= {2} 
  {2} <= {1} 
  {1} < {2} 
  {2} < {1} 
  {1} >= {2} 
  {2} >= {1} 
  {1} > {2} 
  {2} > {1} 
 
All these expressions are true from the definitions above.
Is that reasonable?
It seems a little strange to me.
 
I guess I am very used to strongly ordered things, such that a <= b && a => b implies a == b, not true here, and you can't have both a < b and b < a, which you have here, and that (a < b) == !(a >= b) and similar, which is not true here. In this case, every relation but equality is true.
 
 - Jay
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