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

[Handwerker, Reinhard (ISS Atlanta)]

Peter,
that's not correct, either.
A function (by definition) does not leave out any values in its domain (or
it is not well-defined).
If a function maps every point of its domain one-to-one into the codomain,
it is injective. 
If a function maps every point of its domain onto the codomain (i.e.
assuming every point in the codomain) , it is surjective. 
If a function is both injective and surjective, it is bijective. 
Only a bijective function has an inverse function defined on its codomain.

Reinhard G. Handwerker, Sr. i18n Engineer 
Internet Security Systems, Inc < http://www.iss.net/> +1 404 236 2600 
6303 Barfield Rd,  Atlanta, GA 30328, U.S.A. 
Go i18n@ISS!   
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-----Original Message-----
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Sent: Monday, February 26, 2001 10:19
To: Unicode List
Subject: Re: bijective (was re: An Absurdly Brief Introduction to
Unicode (was



On 02/24/2001 04:43:41 PM Richard Cook wrote:

>Whence does this terminology derive? Set or Mapping theory?

I learned it in high school algebra.


>Anyone
>recommend a definitive text?

I have handy the book from a topology course I took that gives definitions:
Munkres, James A. 1975. Topology: A first course. Prentice-Hall.


>I imagine there are more such terms ...

Of terms, there is no end.


>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 ...

But at least you recognised something that was likely to have been given a
name: surjective.



- Peter


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Peter Constable

Non-Roman Script Initiative, SIL International
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