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Re: An element that contains itself

• From: Michael Kay <mike@saxonica.com>
• To: "Costello, Roger L." <costello@mitre.org>
• Date: Sun, 3 Aug 2014 21:01:20 +0100

> 
> This ENTITY declaration:
> 
> <!ENTITY Set "&A; &B; &Set;">
> 
> says that a Set is an element of itself.

I think you've made a fundamental error here: because you've called your entity "Set", you're imagining that it is a set. But that's not the case. The entity is merely a character string. What you have actually defined here is a character string that contains itself as a substring. To handle this we have to cope with infinite character strings, which gives us practical programming problems, but doesn't lead to any mathematical paradoxes. The analogy with Russell's paradox is a false one, I think.
> 

Michael Kay
Saxonica

• References:
  • An element that contains itself
    • From: "Costello, Roger L." <costello@mitre.org>