Q:

Formal Dirichlet-Bourbaki definition of function

What is the formal Dirichlet-Bourbaki definition of a function?
I have come across this in this essay: http://www.k-12prep.math.ttu.edu/journal/contentknowledge/meel01/article.pdf on page 1.
I know what a function is and I can write down a definition. What I would like to know is what the the definition is that is specifically known as the formal Dirichlet-Bourbaki definition.

A:

A function $f:X\rightarrow Y$ is a subset of $X\times Y$ such that $(x,y_1)\in f$ and $(x,y_2)\in f$ implies $y_1=y_2$.
See for example here: http://books.google.com/books?id=8Wn3SJDIhWwC&pg=PA121&lpg=PA121&dq=dirichlet-bourbaki+function&source=bl&ots=TO_fvKoRy2&sig=RfPmjmSYVJpbeRBOMMadPD8EUNg&hl=en&sa=X&ei=KOxUUbjSIuiaiQLIwIGYBA&ved=0CG4Q6AEwCA#v=onepage&q=dirichlet-bourbaki%20function&f=false

A:

The term "Dirichlet-Bourbaki definition of a function" appears to be a term used by some primary/secondary-level mathematics educators for the contemporary set-theoretic notion of a function. Here is some information about the definitions of Dirichlet and Dedekind, excerpted from Israel Kleiner's article Evolution of the Function Concept: A Brief Survey. See the full article (free) for much more on the complex history.

