Re: Lowercase equivalent to uppercase, or vice versa
- From: "Oliver Wong" <owong@xxxxxxxxxxxxxx>
- Date: Fri, 24 Mar 2006 14:48:38 GMT
"Rick Smith" <ricksmith@xxxxxxx> wrote in message news:12269slsgnij05d@xxxxxxxxxxxxxxxxxxxxx
The clearest description I have found so far
is "asymmetric relation". An asymmetric relation seems
not to be an "equivalence relation", so 'not mathematical
sense' seems about right. Perhaps, logically equivalent then.
(Though Russell is said to have claimed that mathematics
is a branch of logic!)
Yeah, I know of 4 main properties that a "relationship" (in the mathematical sense) can hold (though probably, there exists other interesting properties one could discuss as well):
If we use "A -> B" as a short hand for "A is related to B",
Symmetric: (A -> B) implies (B -> A)
Anti-symmetric: (A -> B) implies NOT(B -> A)
Reflexive: (A -> A)
Transitive: ((A -> B) AND (B -> C)) implies (A -> C)
It's possible for a relation to be not be symmetric and not be anti-symmetric at the same time (e.g. if A -> B and "sometimes" B -> A, as opposed to "always" and "never")
"Equivalence", in the way that I understand it, is symmetric, reflexive and transitive.
- Oliver
.
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