I am working on coming up with a formula, but I am not sure how to
notate the following function:

function(x,y) which returns the lesser of the two values. This is
not for computer use, I just need to know how to notate this correctly
and formally.

Hi adamx-ga,

The standard notation would be "min(x, y)" (as in "minimum").  The
same notation is used for either a series of arguments or a single
argument that is a set.


References:

Wolfram Research's Mathematical Functions web site
http://functions.wolfram.com/ElementaryFunctions/Min/

Page from a Mathematical Logic I course at the University of
Massachusetts
http://www-unix.oit.umass.edu/~klement/513/recursion-a.pdf

A "Review of Basic Prerequisite Mathematics" page from the University
of Toronto
http://www.cs.toronto.edu/~hector/Courses/238F00/prereq.pdf

A paper by Uriel Wittenberg on using mathematical notation in legal
language
http://www.urielw.com/mathlaw/mathlaw.htm#sec34

This notation is also used in various computer programming languages.


Search Strategy:

I suspected that this was the answer from my programming experience
and did some web searching to confirm it.

I already had the "Eric Weisstein's World of Mathematics" web site
open from answering another question, so I used the site's search
function to find the first link listed above, which I consider the
most authoritative.  The others came from Google searches with various
combinations of search terms, of which the most productive were:

minimum mathematical notation "min("

mathematical notation "minimum function"


I hope this information is helpful.

--efn-ga

Thank you.

A simple formula for finding the minimum of two numbers is:

0.5*(x+y-|x-y|)

where |x-y| is the absolute value of x-y.

Thank you for the formula.

In a mathematical proof, I assume it would be more appropriate to use
such a formula than to use the min function. Is that correct?

Thanks again.

min(x,y) is very popular notation, and is definitely "appropriate".
There is no need to complicate your forumla by using 0.5*(x+y-|x-y|)

Thanks for the advice.