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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!

The Power To Protect

-----Original Message-----

From: Peter_Constable@sil.org [mailto:Peter_Constable@sil.org]

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

---------------------------------------------------------------------------

Peter Constable

Non-Roman Script Initiative, SIL International

7500 W. Camp Wisdom Rd., Dallas, TX 75236, USA

Tel: +1 972 708 7485

E-mail: <peter_constable@sil.org>

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