Example:Bijective file conversions

Suppose you are writing a program to convert data from one file format to another (or a function to convert one data structure to another). Such a program describes a function [math]f : A \href{/cs2800/wiki/index.php/%5Cto}{\to} B [/math]. You can think of [math]A [/math] as describing the original file format, and [math]B [/math] as describing the new file format.

It is sensible to check that [math]f [/math] is a bijection. The reason a bijection is desirable is because it has a two-sided inverse [math]g [/math] which can be used to convert the file back into the original format.

If [math]f [/math] is not injective, then it is "lossy": some information about the original file is lost.

If [math]f [/math] is not surjective, then the resulting file format has more data than the original. Further edits to the data in the [math]B [/math] format (in other words, functions from [math]B [/math] to [math]B [/math]) may prevent the object from being mapped back to the original file format.