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last edited 10 years ago by test1 |
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Editor:
Time: 2007/11/17 22:20:23 GMT-8 |
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Note: |
changed: - Equality of sets demands: $$x \in X \iff x \in Y \implies X=Y$$ This axiom fails for the domain 'Set Any'. For example: \begin{axiom} X:Set Any Y:Set Any X:=["x"] Y:=["x"] (X=Y)::Boolean \end{axiom} and \begin{axiom} X:=[1.0] Y:=[1.0] (X=Y)::Boolean \end{axiom} But notice that the following cases work: \begin{axiom} X:=[1] Y:=[1] (X=Y)::Boolean \end{axiom} \begin{axiom} Z:Set Union(String,Integer,Float) W:Set Union(String,Integer,Float) Z:=["x"] W:=["x"] (Z=W)::Boolean \end{axiom}
This axiom fails for the domain Set Any
. For example:
axiomX:Set Any
axiomY:Set Any
axiomX:=["x"]
(1) |
axiomY:=["x"]
(2) |
axiom(X=Y)::Boolean
(3) |
and
axiomX:=[1.0]
(4) |
axiomY:=[1.0]
(5) |
axiom(X=Y)::Boolean
(6) |
But notice that the following cases work:
axiomX:=[1]
(7) |
axiomY:=[1]
(8) |
axiom(X=Y)::Boolean
(9) |
axiomZ:Set Union(String,Integer,Float)
axiomW:Set Union(String,Integer,Float)
axiomZ:=["x"]
(10) |
axiomW:=["x"]
(11) |
axiom(Z=W)::Boolean
(12) |