# Re: Binary Relations, draft 1

• To: Taco Hoekwater <taco.hoekwater@wkap.nl>
• Subject: Re: Binary Relations, draft 1
• From: Hans Aberg <haberg@matematik.su.se>
• Date: Tue, 17 Nov 1998 14:44:00 +0100
• Cc: math-font-discuss@cogs.susx.ac.uk
• Content-Length: 1230

```On the binary relation "134 225D eqdef" symbol (an "=" with the word "def"
above):

For definitions, I decided to use the colon equalities
:=   016 2254 coloneq
=:   017 2255 eqcolon
:=:
all with the word "def" above (and also below). These would be pronounced
:=   defined by
=:   defines
:=:  implicit definition

For example,
x := a + 1  is pronounced "x is defined by a + 1"
a + 1 =: x  is pronounced "a + 1 defines x"
and writing  f(x) + 1 :=: a  means that some quantity in the equation is
implicitly defined by this equation.

The reason is that the symbol "134 225D eqdef" symbol is symmetric, but the
definition is not logically symmetric.

So this is what I decided to use. I have not seen anybody else using it,
but I know that some other mathematicians are prefer an asymmetric
definition symbol. They then use the plain ":=" without any "def" above it.
However, this confuses this symbol with another common meaning, namely
"assignment" in some computer languages.

Hans Aberg
* Email: Hans Aberg <mailto:haberg@member.ams.org>