Re: bijective (was re: An Absurdly Brief Introduction to Unicode (was Re:

From: Richard Cook (rscook@socrates.Berkeley.EDU)
Date: Sat Feb 24 2001 - 18:04:50 EST

Tom Lord wrote:
>> I think I'd like bijective too, if I knew what it meant. Someone?
> It would be a lot more fun to answer this question in plain-text
> Unicode (using math notation) than in ASCII.
> Informally:
> "Bijective" describes a mapping between two sets. Every element of
> the source set ("the domain") is mapped to a unique element of the
> destination set ("the codomain") AND there are no left over elements
> in the codomain. A one to one mapping. An invertible mapping.
> "Injective" describes a mapping where every element of the domain maps
> to a unique element, but there may be left over elements in the
> codomain.
> So, if you have a legacy character set for which Unicode provides a
> loss-less transcoding, then there is an injective mapping from that
> legacy set to Unicode, and, equivalently, a bijective mapping from the
> legacy set to a certain subset of Unicode.
> In the revised version of the absurdly short introduction, I have
> avoided the term "bijective".
> This is now way off topic, so please think twice about following up.
> Thomas Lord

Um, this terminology isn't exactly off-topic, I think. But I see that
neither "Bijective" nor "Injective" are in the Unicode 3.0 glossary.

Whence does this terminology derive? Set or Mapping theory? Anyone
recommend a definitive text? I imagine there are more such terms ...
e.g., what is it called if there are elements left over in the domain
(but not in the codomain)? "Ejective"? I'm feeling "Dejective" for not
knowing these terms already ...

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