Semantics of ==

Terry Reedy tjreedy at udel.edu
Tue Mar 30 22:45:01 EST 2004


"Fred Mailhot" <fred.mailhot at videotron.ca> wrote in message
news:BC8F332F.130C3%fred.mailhot at videotron.ca...

> >>> Consider for instance the following definition:
> >>> * all strings and numbers are called "well-founded"
> >>> * a list is called well-founded if and only if all its elements are
> >>> well-founded.

> Seems to me that the example given makes it clear that l is not
> well-founded.

No.  In my experience, the standard interpretation of such definitions is
that the empty list (in this case) 'trivially satisfies' the condition
precisely because it has no elements to check for conformance.

In pure set theory, sets only have sets as members.  The empty set
'trivially satifies' this condition, to use the standard catchphrase.
Authors vary on whether this sort of this is said explicitly or not.

Terry J. Reedy







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