A list of elements
An algebraic expression
A logic expression
Abstract mathematical notation
A cell in a notebook
A chemical compound
An electric circuit
The /. tells Mathematica to apply a simple transformation rule.
x_ and y_ each stand for any expression, so the pattern x_+ y_ stands for a sum of terms.
Mathematica uses patterns to generalize the notion of functions. This is an ordinary function definition to be used for any x.
Here is a special case that overrides the general definition.
Here is an example of the use of f.
This clears the definitions given for f.
Using patterns allows "functions" to take arguments in any structure.
This specifies the value for the "function" area when given a Circle object as an argument.
This implements a logic reduction rule.