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

From: Handwerker, Reinhard (ISS Atlanta) (
Date: Mon Feb 26 2001 - 11:46:07 EST

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 <> +1 404 236 2600
6303 Barfield Rd, Atlanta, GA 30328, U.S.A.
Go i18n@ISS!
The Power To Protect

-----Original Message-----
From: []
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.

>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: <>

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